Revealing Inconsistencies in X-ray Width Methods for Nanomaterials.
Abstract not provided.
Kunka, Cody↗
SEARCH · Engineering Papers
Results for “numerical method”
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.
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The backward phase flow method for the Eulerian finite time Lyapunov exponent computations
We propose a simple Eulerian approach to compute the moderate to long time flow map for approximating the Lyapunov exponent of a (periodic or aperiodic) dynamical system. The idea is to generalize a recently proposed backward phase flow method which is specially designed for long time level set propagation. Unlike the original phase flow method or the backward phase flow method, which is applicable only to autonomous systems, the current approach can also be applied to any time-dependent (periodic or aperiodic) flow. We will discuss the stability of the proposed method. Numerical examples will be given to demonstrate the effectiveness of the algorithm.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Closed-Form Solutions for the Equations of Motion of the Heavy Symmetrical Top with One Point Fixed
The Equations of Motion (EOM) for the Heavy Symmetrical Top with One Point Fixed are highly non-linear. The literature describes the numerical methods that are used to resolve this Classical system including modern tools i.e. the Runge-Kutta Fourth Order method. It is more difficult to derivate closed-form solutions for the EOM and as mentioned in the literature it is not always possible to find the close-form solution for all the EOM. Fortunately, there are a few examples available that will serve as a guide to move further on in this topic. It is the purpose of this paper to find a methodology that will produce the solutions for a given subset of EOM that fulfill certain requisites. The report is organized as follows: it starts with a very short summary of the literature available on this topic and quickly follows into the derivation of the EOM using the Euler-Lagrange method. The Routhian will be used to reduce the size of the expression. It continues with the formulation of the Classical cubic function (f(u)) through a novel process. The roots of f(u) are of the outmost importance to be able to find the EOM closed-form solution, and once the final roots are selected the general method that will produce the closed-form solutions is presented. Two sets of examples are included to show the validity of the process and comparisons of the results from the closed-form solutions vs. the numerical results for these examples are shown.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Rolling Element Bearing Stiffness Matrix Determination (Presentation)
Current theoretical bearing models differ in their stiffness estimates because of different model assumptions. In this study, a finite element/contact mechanics model is developed for rolling element bearings with the focus of obtaining accurate bearing stiffness for a wide range of bearing types and parameters. A combined surface integral and finite element method is used to solve for the contact mechanics between the rolling elements and races. This model captures the time-dependent characteristics of the bearing contact due to the orbital motion of the rolling elements. A numerical method is developed to determine the full bearing stiffness matrix corresponding to two radial, one axial, and two angular coordinates; the rotation about the shaft axis is free by design. This proposed stiffness determination method is validated against experiments in the literature and compared to existing analytical models and widely used advanced computational methods. The fully-populated stiffness matrix demonstrates the coupling between bearing radial, axial, and tilting bearing deflections.
17 WIND ENERGY↗
Closed-Form Solutions for the Equations of Motion of the Heavy Symmetrical Top with One Point Fixed
The equations of motion (EOM) for the heavy symmetrical top with one point fixed are highly nonlinear. The literature describes the numerical methods that are used to resolve this classical system, including modern tools, such as the Runge–Kutta fourth–order method. Finding the derivate of closed-form solutions for the EOM is more difficult and, as mentioned in the literature, discovering the solution is not always possible for all the EOM. Fortunately, a few examples are available that serve as a guide to move further in this topic. The purpose of this paper is to find a methodology that will produce the solutions for a given subset of EOMs that fulfill certain requisites. This paper summarizes the literature available on this topic and then follows with the derivation of the EOM using the Euler–Lagrange method. The Routhian method will be used to reduce the size of the expression, and it continues with the formulation of the classical cubic function, ƒ(u), through a novel process. The roots of ƒ(u) are of the utmost importance in finding the EOM closed-form solution, and once the final roots are selected, the general method that will produce the closed-form solutions is presented. Two sets of examples are included to show the validity of the process, and comparisons of the results from the closed-form solutions vs. the numerical results for these examples are shown.
Laos, Hector↗
Novel methods in the Particle-In-Cell accelerator Code-Framework Warp
The Particle-In-Cell (PIC) Code-Framework Warp is being developed by the Heavy Ion Fusion Science Virtual National Laboratory (HIFS-VNL) to guide the development of accelerators that can deliver beams suitable for high-energy density experiments and implosion of inertial fusion capsules. It is also applied in various areas outside the Heavy Ion Fusion program to the study and design of existing and next-generation high-energy accelerators, including the study of electron cloud effects and laser wakefield acceleration for example. This study presents an overview of Warp's capabilities, summarizing recent original numerical methods that were developed by the HIFS-VNL (including PIC with adaptive mesh refinement, a large-timestep 'drift-Lorentz' mover for arbitrarily magnetized species, a relativistic Lorentz invariant leapfrog particle pusher, simulations in Lorentz-boosted frames, an electromagnetic solver with tunable numerical dispersion and efficient stride-based digital filtering), with special emphasis on the description of the mesh refinement capability. In addition, selected examples of the applications of the methods to the abovementioned fields are given.
43 PARTICLE ACCELERATORS↗
Sensitivities and Uncertainties Related to Numerics and Building Features in Urban Modeling
Oak Ridge National Laboratory (ORNL) has been engaged in the development and testing of a computational system that would use a grid of activation foil detectors to provide postdetonation forensic information from a nuclear device detonation. ORNL has developed a high-performance, three-dimensional (3-D) deterministic radiation transport code called Denovo. Denovo solves the multigroup discrete ordinates (SN) equations and can output 3-D data in a platform-independent format that can be efficiently analyzed using parallel, high-performance visualization tools. To evaluate the sensitivities and uncertainties associated with the deterministic computational method numerics, a numerical study on the New York City Times Square model was conducted using Denovo. In particular, the sensitivities and uncertainties associated with various components of the calculational method were systematically investigated, including (a) the Legendre polynomial expansion order of the scattering cross sections, (b) the angular quadrature, (c) multigroup energy binning, (d) spatial mesh sizes, (e) the material compositions of the building models, (f) the composition of the foundations upon which the buildings rest (e.g., ground, concrete, or asphalt), and (g) the amount of detail included in the building models. Although Denovo may calculate the idealized model well, there may be uncertainty in the results because of slight departures of the above-named parameters from those used in the idealized calculations. Fluxes and activities at selected locations from perturbed calculations are compared with corresponding values from the idealized or base case to determine the sensitivities associated with specified parameter changes. Results indicate that uncertainties related to numerics can be controlled by using higher fidelity models, but more work is needed to control the uncertainties related to the model.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations
We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Multiscale Modeling using Molecular Dynamics and Dual Domain Material Point Method
For problems involving large material deformation rate, the material deformation time scale can be shorter than the material takes to reach a thermodynamical equilibrium. For such problems, it is difficult to obtain a constitutive relation. History dependency become important because of thermodynamic non-equilibrium. Our goal is to build a multi-scale numerical method which can bypass the need for a constitutive relation. In conclusion, multi-scale simulation method is developed based on the dual domain material point (DDMP). Molecular dynamics (MD) simulation is performed to calculate stress. Since the communication among material points is not necessary, the computation can be done embarrassingly parallel in CPU-GPU platform.
36 MATERIALS SCIENCE↗
Time-dependent THMC properties and microstructural evolution of damaged rocks in excavation damage zone
Modeling coupled thermo-hydro-mechanical-chemical (THMC) processes in host rocks near high-level nuclear waste (HLW) repositories at various time scales is an extremely challenging task. The current study integrates experimental, theoretical, and numerical methods in assessing the evolution of excavation damage zone (EDZ) over time and its implication on the long-term migration of hazardous species. Argillite and rock salt and are the focus of this study. The first part of the report presents a novel time-dependent directional microcrack damage theory for generic brittle rocks. It features detailed statistical description of the microcracks within a damaged solid, permitting a direct upscaling of microscale processes such as crack growth kinetics, crack closure/opening, sliding friction to explain the macroscopic creep, nonlinear elasticity, shear dilation, and loading-unloading hysteresis. This provides a basic platform for describing the anisotropic mechanical and transport properties of damaged rocks during excavation and subsequent THMC loadings. The model is validated and numerically implemented to Finite Element (FE) package ABAQUS through the user-defined material (UMAT) interface and have demonstrated great potential in resolving the time-dependent and anisotropic evolution of damage in the EDZ. The second part of the report presents a multi-scale experimental effort in characterizing the thermal, hydraulic, and mechanical properties of Mancos shale and Avery Island salt. For the Mancos shale, triaxial compression tests are performed at different confining pressures and temperatures to probe its thermomechanical properties relevant to HLW repositories. The obtained stress-strain data are interpreted using the proposed directional damage theory. Post-test specimens are subjected to gas permeability tests to reveal the correlation between permeability and the degree of microcracking. At microscale, temperature-controlled nanoindentation tests are performed and found a linear correlation between fracture toughness and elastic modulus from 25°C to 300°C. For Avery Island salt, we have designed and manufactured a novel relative-humidity controlled uniaxial creep device. Long-term creep tests at low stresses (< 5 MPa) are performed at different levels of relative humidity (RH). Besides confirming the much higher creep rates as one would expect through extrapolating the high-stress creep data, the results reveal that the steady-state creep rate of rock salt is strongly dependent on the ambient RH, an aspect that is often neglected in the literature. Both behaviors can be attributed to the pressure-solution creep mechanism which dominates at low stress and high RH levels. The third part of the report explores a set of numerical strategies in modeling the THMC behavior of porous geomaterials. A fully implicit, monolithic FE solution that can flexibly interface with different material models and coupling mechanisms for THMC problems is developed and verified through the ABAQUS user-defined element (UEL) interface. The scheme is used to study the THM response of a hypothetical HLW storage site with reference to an existing in-situ heater test. Strategies for integrating the UEL and the microcrack UMAT are suggested. Another numerical endeavor of this study is to implement a higher-order asymptotic homogenization method to account for the heterogeneous porous structures. The same method is then extended to perform microstructure-informed thermo-mechanical modeling of generalized continua. The above outcomes of this project provide a strong thrust towards enhancing the fundamental understanding and modeling capability of the long-term evolution of host rocks in EDZ, thus helping achieve the design goal of 1-million-year isolation of high-level nuclear wastes.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Cone-grid scheme for solving hyperbolic systems of conservation laws and one application
In this work, we introduce a new numerical method, the so-called cone-grid scheme for solving hyperbolic systems of conservation laws. The formulation and the theoretical analysis for this scheme are slightly simpler than other algorithms. Simultaneously, our technique leads to a more efficacious numerical scheme. The Riemann solution is the basic ingredient for this scheme. We also give the main application of this technique, namely the global weak solutions for the one-dimensional model prescribes heat conduction in solids at low temperature, which called phonon–Bose model. This system consists of a conservation equation for the energy density and the heat flux. The scheme also satisfies positivity. The cone-grid scheme was compared with exact solution by three numerical examples, where explicit solutions are known. These numerical results verify the accuracy of the proposed scheme qualitatively and quantitatively.
97 MATHEMATICS AND COMPUTING↗
Fast calculation of diffraction patterns from an ensemble of aligned molecules
We report an algorithm to calculate electron diffraction patterns for molecules with anisotropic angular distribution, which is significantly faster than existing methods. The algorithm uses a transform to convert the molecular orientation distribution, which is a function of three Euler angles, to the atom-pair distribution functions which depend on the polar and azimuthal angles. The diffraction signal can then be calculated from the atom-pair distributions. We demonstrate the computation method numerically by calculating electron diffraction patterns for a symmetric top molecule (trifluoroiodomethane) and an asymmetric top molecule (formaldehyde) and show that it reduces the calculation time by approximately two orders of magnitude compared to the standard brute-force method. Here, the method can also be applied to the calculation of x-ray diffraction patterns.
74 ATOMIC AND MOLECULAR PHYSICS↗
Recent Progress in Nonlinear and Linear Solvers
We discuss two approaches for tackling algebraic systems, one is based on block preconditioning and the other is based on multifrontal and hierarchical matrix methods. First we consider a new preconditioner framework for supporting implicit time integration within an atmospheric climate model. We give an overview of the computational infrastructure used in atmospheric climate studies, address specific challenges of weak-scalability of numerical methods used in these codes, outline a strategy for addressing these challenges, and provide details about the software infrastructure being developed to implement these ideas. In the second part, we present our recent results of employing hierarchically semiseparable low-rank structure in a multifrontal factorization framework. This leads to superfast linear solvers for elliptic PDEs and effective preconditioners for a wider class of sparse linear systems.
54 ENVIRONMENTAL SCIENCES↗
Evaluation of Analytical and Numerical Techniques for Defining the Radius of Influence for an Open-Loop Ground Source Heat Pump System
In an open-loop groundwater heat pump (GHP) system, groundwater is extracted, run through a heat exchanger, and injected back into the ground, resulting in no mass balance changes to the flow system. Although the groundwater use is non-consumptive, the withdrawal and injection of groundwater may cause negative hydraulic and thermal impacts to the flow system. Because GHP is a relatively new technology and regulatory guidelines for determining environmental impacts for GHPs may not exist, consumptive use metrics may need to be used for permit applications. For consumptive use permits, a radius of influence is often used, which is defined as the radius beyond which hydraulic impacts to the system are considered negligible. In this paper, the hydraulic radius of influence concept was examined using analytical and numerical methods for a non-consumptive GHP system in southeastern Washington State. At this location, the primary hydraulic concerns were impacts to nearby contaminant plumes and a water supply well field. The results of this study showed that the analytical techniques with idealized radial flow were generally unsuited because they over predicted the influence of the well system. The numerical techniques yielded more reasonable results because they could account for aquifer heterogeneities and flow boundaries. In particular, the use of a capture zone analysis was identified as the best method for determining potential changes in current contaminant plume trajectories. The capture zone analysis is a more quantitative and reliable tool for determining the radius of influence with a greater accuracy and better insight for a non-consumptive GHP assessment.
GHPs↗
Large-eddy simulation of turbulent cavitating flow in a micro channel
Large-eddy simulations (LES) of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented. Two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of the liquid and the liquid-vapor mixture is taken into account. The Adaptive Local Deconvolution Method (ALDM), adapted for cavitating flows, is employed for discretizing the convective terms of the Navier-Stokes equations for the homogeneous mixture. ALDM is a finite-volume-based implicit LES approach that merges physically motivated turbulence modeling and numerical discretization. Validation of the numerical method is performed for a cavitating turbulent mixing layer. Comparisons with experimental data of the throttle flow at two different operating conditions are presented. The LES with the employed cavitation modeling predicts relevant flow and cavitation features accurately within the uncertainty range of the experiment. The turbulence structure of the flow is further analyzed with an emphasis on the interaction between cavitation and coherent motion, and on the statistically averaged-flow evolution.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Non-adiabatic molecular dynamics of molecules in the presence of strong light-matter interactions
When the interaction between a molecular system and confined light modes in an optical or plasmonic cavity is strong enough to overcome the dissipative process, hybrid light-matter states (polaritons) become the fundamental excitations in the system. The mixing between the light and matter characters modifies the photophysical and photochemical properties. Notably, it was reported that these polaritons can be employed to control photochemical reactions, charge and energy transfer, and other processes. In addition, according to recent studies, vibrational strong coupling can be employed to resonantly enhance the thermally-activated chemical reactions. In this work, a theoretical model and an efficient numerical method for studying the dynamics of molecules strongly interacting with quantum light are developed based on nonadiabatic excited-state molecular dynamics. The methodology was employed to study the cis-trans photoisomerization of a realistic molecule in a cavity. Numerical simulations demonstrate that the photochemical reactions can be controlled by tuning the properties of the cavity. In the calculated example, the isomerization is suppressed when polaritonic states develop a local minimum on the lower polaritonic state. Moreover, the observed reduction of isomerization is tunable via the photon energy and light-molecule coupling strength. However, the fluctuation in the transition dipole screens the effect of light-matter, which makes it harder to tune the photochemical properties via the coupling strength. These insights gained from this study suggest quantum control of photochemical reactions is possible by specially designed photonic or plasmonic cavities.
36 MATERIALS SCIENCE↗
TomoBank: a tomographic data repository for computational x-ray science
There is a widening gap between the fast advancement of computational methods for tomographic reconstruction and their successful implementation in production software at various synchrotron facilities. This is due in part to the lack of readily available instrument datasets and phantoms representative of real materials for validation and comparison of new numerical methods. Recent advancements in detector technology made sub-second and multi-energy tomographic data collection possible [1], but also increased the demand to develop new reconstruction methods able to handle in-situ [2] and dynamic systems [3] that can be quickly incorporated in beamline production software [4]. The X-ray Tomography Data Bank, tomoBank, provides a repository of experimental and simulated datasets with the aim to foster collaboration among computational scientists, beamline scientists, and experimentalists and to accelerate the development and implementation of tomographic reconstruction methods for synchrotron facility production software by providing easy access to challenging dataset and their descriptors.
96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
Improved performance of HgCdTe infrared detector focal plane arrays by modulating light field based on photonic crystal structure
An HgCdTe long-wavelength infrared focal plane array photodetector is proposed by modulating light distributions based on the photonic crystal. It is shown that a promising prospect of improving performance is better light harvest and dark current limitation. To optimize the photon field distributions of the HgCdTe-based photonic crystal structure, a numerical method is built by combining the finite-element modeling and the finite-difference time-domain simulation. The optical and electrical characteristics of designed HgCdTe mid-wavelength and long-wavelength photon-trapping infrared detector focal plane arrays are obtained numerically. The results indicate that the photon crystal structure, which is entirely compatible with the large infrared focal plane arrays, can significantly reduce the dark current without degrading the quantum efficiency compared to the regular mesa or planar structure.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗