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At least 1,117 records · Page 62
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Computer simulation of impurity diffusion in silicon, part 1

The elementary classical models for idealized diffusion conditions are described, and the principles are then used in developing more realistic models. The practical models require some type of numerical analysis. The numerical techniques are outlined and details concerning their implementation are given. Some results are presented which were obtained with the computer programs implementing the numerical techniques with implicit and explicit methods. Special problems of impurity-rich interlayers forming between an oxide and silicon are considered. A set of computed curves for sheet resistance, junction depth, and oxide thickness for different diffusion schedules is included.

Gassaway, J. D.↗
NASA NTRS1976

Inverse atmospheric radiative transfer problems - A nonlinear minimization search method of solution

The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.

Fymat, A. L.↗
DOE OSTI2017

Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green’s function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as “black-box” simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Physical and mechanical metallurgy of zirconium alloys for nuclear applications: a multi-scale computational study

In the post-Fukushima world, the stability of materials under extreme conditions is an important issue for the safety of nuclear reactors. Because the nuclear industry is going to continue using advanced zirconium cladding materials in the foreseeable future, it become critical to gain fundamental understanding of the several interconnected problems. First, what are the thermodynamic and kinetic factors affecting the oxidation and hydrogen pick-up by these materials at normal, off-normal conditions, and in long-term storage? Secondly, what protective coatings (if any) could be used in order to gain extremely valuable time at off-normal conditions, e.g., when temperature exceeds the critical value of 2200°F? Thirdly, the kinetics of oxidation of such protective coating or braiding needs to be quantified. Lastly, even if some degree of success is achieved along this path, it is absolutely critical to have automated inspection algorithms allowing identifying defects of cladding as soon as possible. This work strives to explore these interconnected factors from the most advanced computational perspective, utilizing such modern techniques as first-principles atomistic simulations, computational thermodynamics of materials, diffusion modeling, and the morphological algorithms of image processing for defect identification. Consequently, it consists of the four parts dealing with these four problem areas preceded by the introduction and formulation of the studied problems. In the 1st part an effort was made to employ computational thermodynamics and ab initio calculations to shed light upon the different stages of oxidation of ziraloys (2 and 4), the role of microstructure optimization in increasing their thermal stability, and the process of hydrogen pick-up, both in normal working conditions and in long-term storage. The 2nd part deals with the need to understand the influence and respective roles of the two different plasticity mechanisms in Zr nuclear alloys: twinning (at low T) and crystallographic slip (higher T’s). For that goal, a description of the advanced plasticity model is outlined featuring the non-associated flow rule in hcp materials including Zr. The 3rd part describes the kinetic theory of oxidation of the several materials considered to be perspective coating materials for Zr alloys: SiC and ZrSiO 4 . In the 4th part novel and advanced projectional algorithms for defect identification in zircaloy coatings are described. In so doing, the author capitalized on some 12 years of his applied industrial research in this area. Our conclusions and recommendations are presented in the 5th part of this work, along with the list of used literature and the scripts for atomistic, thermodynamic, kinetic, and morphological computations.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Acceleration of diffusive molecular dynamics simulations through mean field approximation and subcycling time integration

Highlights: • Two numerical methods are presented to accelerate DMD simulations. • The methods greatly reduce the computation time without much loss of accuracy. • The accelerated DMD model is capable of simulating long-term mass transport at atomistic length scales. • Demonstrated for the propagation of an atomically sharp phase boundary over 30 seconds. - Abstract: Diffusive Molecular Dynamics (DMD) is a class of recently developed computational models for the simulation of long-term diffusive mass transport at atomistic length scales. Compared to previous atomistic models, e.g., transition state theory based accelerated molecular dynamics, DMD allows the use of larger time-step sizes, but has a higher computational complexity at each time-step due to the need to solve a nonlinear optimization problem at every time-step. This paper presents two numerical methods to accelerate DMD based simulations. First, we show that when a many-body potential function, e.g., embedded atom method (EAM), is employed, the cost of DMD is dominated by the computation of the mean of the potential function and its derivatives, which are high-dimensional random variables. To reduce the cost, we explore both first- and second-order mean field approximations. Specifically, we show that the first-order approximation, which uses a point estimate to calculate the mean, can reduce the cost by two to three orders of magnitude, but may introduce relatively large error in the solution. We show that adding an approximate second-order correction term can significantly reduce the error without much increase in computational cost. Second, we show that DMD can be significantly accelerated through subcycling time integration, as the cost of integrating the empirical diffusion equation is much lower than that of the optimization solver. To assess the DMD model and the numerical approximation methods, we present two groups of numerical experiments that simulate the diffusion of hydrogen in palladium nanoparticles. In particular, we show that the computational framework is capable of capturing the propagation of an atomically sharp phase boundary over a time window of more than 30 seconds. The effects of the proposed numerical methods on solution accuracy and computation time are also assessed quantitatively.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Turbulence-induced relative velocity of dust particles. III. The probability distribution

Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, τ{sub p1} and τ{sub p2}, of two particles of arbitrary sizes. The friction time of the particles included in the simulation ranges from 0.1τ{sub η} to 54T {sub L}, where τ{sub η} and T {sub L} are the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically non-Gaussian, exhibiting fat tails. For a fixed value of τ{sub p1}, the PDF shape is the fattest for equal-size particles (τ{sub p2} = τ{sub p1}), and becomes thinner at both τ{sub p2} < τ{sub p1} and τ{sub p2} > τ{sub p1}. Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in (1/2) ≲ f ≲ 1, the PDF fatness first increases with the friction time τ{sub p,h} of the larger particle, peaks at τ{sub p,h} ≅ τ{sub η}, and then decreases as τ{sub p,h} increases further. For 0 ≤ f ≲ (1/4), the PDF becomes continuously thinner with increasing τ{sub p,h}. The PDF is nearly Gaussian only if τ{sub p,h} is sufficiently large (>>T {sub L}). These features are successfully explained by the Pan and Padoan model. Using our simulation data and some simplifying assumptions, we estimated the fractions of collisions resulting in sticking, bouncing, and fragmentation as a function of the dust size in protoplanetary disks, and argued that accounting for non-Gaussianity of the collision velocity may help further alleviate the bouncing barrier problem.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

An effective numerical algorithm for intra-granular fission gas release during non-equilibrium trapping and resolution

Both fission gas release and gaseous swelling in nuclear fuel are driven by the transport of fission gas from within the fuel grains to grain boundaries (intra-granular fission gas release). The process involves gas atom diffusion in conjunction with trapping in and resolution from intra-granular bubbles, and is described mathematically by a system of two partial differential equations (PDE). Following Speight, under the assumption of equilibrium between trapping and resolution (quasi-stationary approximation) the system can be reduced to a single diffusion equation with an effective diffusion coefficient. Numerical solutions used in engineering fuel performance calculations invariably rely on this simplification. First, we investigate the validity of the quasi-stationary approximation compared to the solution of the general system of PDEs. Results demonstrate that the approximation is valid under most conditions of practical interest, but is inadequate to model intra-granular fission gas release during rapid transients to relatively high temperatures such as postulated reactivity initiated accidents (RIA). Then, we develop a novel numerical algorithm for the solution of the general problem in time-varying conditions. We verify the PolyPole-2 algorithm against a reference finite difference solution for a large number of randomly generated operation histories including prototypical RIA transients. Results demonstrate that PolyPole-2 captures the solution of the general PDE system with a high accuracy and a low computational cost. As a result, the PolyPole-2 algorithm overcomes the quasi-stationary approximation and the concept of an effective diffusion coefficient for the solution of the intra-granular fission gas release problem in nuclear fuel analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1983

The problem of cooling the cold Io torus

Two models are developed for the transport of ions inward from Io's orbit, the first using the assumption that radial diffusion is the dominant transport mechanism while the second uses a combination of diffusive and convective transport. The models include thermal and number density transport, radiation, ionization and pickup of local neutrals, recombination, charge exchange, and Coulomb interactions. It is found that pure diffusive transport can account for the dramatic inward depletion of the torus only by invoking recombination or by postulating a massive increase in the production rate of torus ions sometime prior to the Voyager mission. Recombination is determined to be far too slow to be the cause of the observed density decrease inside of Io. The model combining convection and diffusion is shown to reasonably match the data, but only if a diffusion coefficient 100 times less than that derived from Pioneer observations is used. In addition, it is shown that the Pioneer derived diffusion rate combined with Voyager temperature and density measurements indicate a large nonradiative sink of energy in the inner torus.

Richardson, J. D.↗
DOE OSTI2021

Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

Under compressive creep, viscoplastic solids experiencing internal mass transfer processes can accommodate singular cnoidal wave solutions as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the material's capacity to diffusive internal perturbations, leading to localized failure features (e.g., cracks and compaction bands). These cnoidal waves, generally found in fluids, have strong nonlinearities that produce periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, practical simulation tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This automatic refinement method provides an error estimate that drives mesh adaptivity, a crucial feature for the problem at hand. We compare the performance of this adaptive strategy against analytical and standard finite element solutions. We then investigate the sensitivity of the diffusivity ratio, the parameter controlling the process, and identify multiple possible solutions with several stress peaks. We also show the evolution of the spacing between peaks for all solutions as a function of that parameter.

42 ENGINEERING↗
DOE OSTI2022

Verification of the AGREE and Serpent for the steady state HTR-10 benchmark problems

This paper provides results from steady state HTR-10 benchmark calculations performed using AGREE and Serpent that are compared to experimental results as well as calculations performed by INET. The purpose of completing this benchmark is to validate AGREE and Serpent for the prediction of HTGR operation so that they may ultimately be used to support licensing and deployment efforts of advanced reactors. The benchmark consists of several problems ranging from control rod worth calculations to k{sub eff} calculations at various temperatures. Overall, AGREE and Serpent show good agreement with the reference solutions and are effectively able to predict HTGR operation for a variety of steady state cases. The largest difference from the reference was for the initial core single rod worth, which is possibly due to the larger core helium cavity causing inaccuracies in the diffusion calculation whereas the control rod worth determined by Serpent and AGREE is much closer to the reference result for the full core loading. Moreover, in every benchmark problem, increasing the number of energy groups in the cross sections results in improved agreement of the AGREE result with the reference, although it also causes an increase in computation time. For problems with experimental data available, the accuracy of results generated by Serpent and AGREE is comparable to results obtained by other benchmark participants. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1975

A cubic spline approximation for problems in fluid mechanics

A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

Rubin, S. G.↗
DOE OSTI2021

Connectivity‐based parcellation of normal and anatomically distorted human cerebral cortex

Abstract For over a century, neuroscientists have been working toward parcellating the human cortex into distinct neurobiological regions. Modern technologies offer many parcellation methods for healthy cortices acquired through magnetic resonance imaging. However, these methods are suboptimal for personalized neurosurgical application given that pathology and resection distort the cerebrum. We sought to overcome this problem by developing a novel connectivity‐based parcellation approach that can be applied at the single‐subject level. Utilizing normative diffusion data, we first developed a machine‐learning (ML) classifier to learn the typical structural connectivity patterns of healthy subjects. Specifically, the Glasser HCP atlas was utilized as a prior to calculate the streamline connectivity between each voxel and each parcel of the atlas. Using the resultant feature vector, we determined the parcel identity of each voxel in neurosurgical patients ( n = 40) and thereby iteratively adjusted the prior. This approach enabled us to create patient‐specific maps independent of brain shape and pathological distortion. The supervised ML classifier re‐parcellated an average of 2.65% of cortical voxels across a healthy dataset ( n = 178) and an average of 5.5% in neurosurgical patients. Our patient dataset consisted of subjects with supratentorial infiltrating gliomas operated on by the senior author who then assessed the validity and practical utility of the re‐parcellated diffusion data. We demonstrate a rapid and effective ML parcellation approach to parcellation of the human cortex during anatomical distortion. Our approach overcomes limitations of indiscriminately applying atlas‐based registration from healthy subjects by employing a voxel‐wise connectivity approach based on individual data.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

A new continuum approach for nonlinear kinetic simulation and transport analysis

A numerical code based on the I-transform approach is developed to solve the nonlinear Vlasov equation and carry out the transport analysis. The numerical results given by the I-transform approach agree with the conservative semi-Lagrangian approach in the Landau damping case and the bump-on-tail instability case. The diffusivities induced by the random fields and the quasilinear transport are also successfully demonstrated by using the new approach. It is found that the nonlinear transport in the one-dimensional Langmuir turbulence cannot be well-described by a simple diffusion model, due to the strong particle trapping at the nonlinear stage.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Interaction-induced backscattering in short quantum wires

We study interaction-induced backscattering in clean quantum wires with adiabatic contacts exposed to a voltage bias. Particle backscattering relaxes such systems to a fully equilibrated steady state only on length scales exponentially large in the ratio of bandwidth of excitations and temperature. Here in this paper we focus on shorter wires in which full equilibration is not accomplished. Signatures of relaxation then are due to backscattering of hole excitations close to the band bottom which perform a diffusive motion in momentum space while scattering from excitations at the Fermi level. This is reminiscent to the first passage problem of a Brownian particle and, regardless of the interaction strength, can be described by an inhomogeneous Fokker-Planck equation. From general solutions of the latter we calculate the hole backscattering rate for different wire lengths and discuss the resulting length dependence of interaction-induced correction to the conductance of a clean single channel quantum wire.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Real-Time Control of an Ensemble of Heterogeneous Resources

This paper focuses on the problem of controlling an ensemble of heterogeneous resources connected to an electrical grid at the same point of common coupling (PCC). The controller receives an aggregate power setpoint for the ensemble in real time and tracks this setpoint by issuing individual optimal setpoints to the resources. The resources can have continuous or discrete nature (e.g., heating systems consisting of a finite number of heaters that each can be either switched on or off) and/or can be highly uncertain (e.g., photovoltaic (PV) systems or residential loads). A naive approach would lead to a stochastic mixed-integer optimization problem to be solved at the controller at each time step, which might be infeasible in real time. Instead, we allow the controller to solve a continuous convex optimization problem and compensate for the errors at the resource level by using a variant of the well-known error diffusion algorithm. We give conditions guaranteeing that our algorithm tracks the power setpoint at the PCC on average while issuing optimal setpoints to individual resources. We illustrate the approach numerically by controlling a collection of batteries, PV systems, and discrete loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Features of the structural states of KNbO{sub 3} single crystals before and after fast-neutron irradiation

Neutron irradiation is a unique tool for forming new structural states of ferroelectrics, which cannot be obtained by conventional methods. The inf luence of the irradiation by two doses of fast neutrons (F = 1 × 10{sup 17} and 3 × 10{sup 17} cm{sup –2}) on the structure and properties of KNbO{sub 3} single crystals has been considered for the first time. The developed method for taking into account the experimental correction to the diffuse scattering has been used to analyze the structural changes occurring in KNbO{sub 3} samples at T = 295 K and their correlations with the behavior of dielectric and nonlinear optical characteristics. The irradiation to the aforementioned doses retains the KNbO{sub 3} polar structure, shifting Т{sub Ð}¡ to lower temperatures and significantly affecting only the thermal parameters and microstructure of single crystals. Neutron irradiation with small atomic displacements provides a structure similar to the high-temperature modification of an unirradiated KNbO{sub 3} crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Specificities of one-dimensional dissipative magnetohydrodynamics

One-dimensional dynamics of a plane slab of cold (β ≪ 1) isothermal plasma accelerated by a magnetic field is studied in terms of the MHD equations with a finite constant conductivity. The passage to the limit β → 0 is analyzed in detail. It is shown that, at β = 0, the character of the solution depends substantially on the boundary condition for the electric field at the inner plasma boundary. The relationship between the boundary condition for the pressure at β > 0 and the conditions for the electric field at β = 0 is found. The stability of the solution against one-dimensional longitudinal perturbations is analyzed. It is shown that, in the limit β → 0, the stationary solution is unstable if the time during which the acoustic wave propagates across the slab is longer than the time of magnetic field diffusion. The growth rate and threshold of instability are determined, and results of numerical simulation of its nonlinear stage are presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Density-Equalizing Maps for Simply Connected Open Surfaces

Here in this paper, we are concerned with the problem of creating flattening maps of simply connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing maps with any prescribed density distribution. By varying the initial density distribution, a large variety of flattening maps with different properties can be achieved. For instance, area-preserving parameterizations of simply connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored.

97 MATHEMATICS AND COMPUTING↗