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DOE OSTI2017

Testing approximate predictions of displacements of cosmological dark matter halos

We present a test to quantify how well some approximate methods, designed to reproduce the mildly non-linear evolution of perturbations, are able to reproduce the clustering of DM halos once the grouping of particles into halos is defined and kept fixed. The following methods have been considered: Lagrangian Perturbation Theory (LPT) up to third order, Truncated LPT, Augmented LPT, MUSCLE and COLA. The test runs as follows: halos are defined by applying a friends-of-friends (FoF) halo finder to the output of an N-body simulation. The approximate methods are then applied to the same initial conditions of the simulation, producing for all particles displacements from their starting position and velocities. The position and velocity of each halo are computed by averaging over the particles that belong to that halo, according to the FoF halo finder. This procedure allows us to perform a well-posed test of how clustering of the matter density and halo density fields are recovered, without asking to the approximate method an accurate reconstruction of halos. We have considered the results at z =0,0.5,1, and we have analysed power spectrum in real and redshift space, object-by-object difference in position and velocity, density Probability Distribution Function (PDF) and its moments, phase difference of Fourier modes. We find that higher LPT orders are generally able to better reproduce the clustering of halos, while little or no improvement is found for the matter density field when going to 2LPT and 3LPT. Augmentation provides some improvement when coupled with 2LPT, while its effect is limited when coupled with 3LPT. Little improvement is brought by MUSCLE with respect to Augmentation. The more expensive particle-mesh code COLA outperforms all LPT methods, and this is true even for mesh sizes as large as the inter-particle distance. This test sets an upper limit on the ability of these methods to reproduce the clustering of halos, for the cases when these objects are reconstructed at the object-by-object level.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

A higher order approximate static condensation method for multi-material diffusion problems

The paper studies an approximate static condensation method for the diffusion problem with discontinuous diffusion coefficients. The method allows for a general polygonal mesh which is unfitted to the material interfaces. Moreover, the interfaces can be discontinuous across the mesh edges as typical for numerical reconstructions using the volume or moment-of-fluid methods. We apply a mimetic finite difference method to solve local diffusion problems and use P 1 (mortar) edge elements to couple local problems into the global system. The condensation process and the properties of the resulting algebraic system are discussed. It is demonstrated that the method is second order accurate on smooth solutions and performs well for problems with high contrast in diffusion coefficients. Experiments also show the robustness with respect to position of the material interfaces against the underlying mesh.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Efficient manifolds tracing for planar maps

Here, we present an exact calculation method and an approximation technique for tracing the invariant manifolds of unstable periodic orbits of planar maps. The exact approach relies on an adaptive refinement procedure that prevents redundant calculations occurring in other approaches, and the approximated method relies on a novel interpolation approach based on normal displacement functions. The resulting approximated manifold is precise when compared to the exact one, and its relative computational cost falls like the inverse of the manifold length. To present the tracing method, we obtain the invariant manifolds of the Chirikov-Taylor map, and as an application we illustrate the transition from homoclinic to heteroclinic chaos in the Duffing oscillator that leads from localized chaos to global chaotic motion.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2016

Mammograms restoration by using Wiener filter

Restoration of digital mammograms, as a pre-processing tool, using deconvolution procedures, is analysed. It implies, knowing Modulation Transfer Function (MTF) of the mammography device and the estimation of the mammogram’s noise. Wiener filter is used, as the most objective in mammograms restoration by deconvolution. Using MATLAB program the deconvolution procedures are conducted in two ways with different level of approximation. The first method approximates the noise/signal power ratio by a constant and the second method uses autocorrelation functions of the noise and signals. Abilities and limitations of the methods are analysed and checked by using the raw images of the bar-pattern due to better visualisation of the obtained results. The raw images are obtained at a Computed Radiography (CR) mammography device in Clinical Centre in Podgorica. It is found that quality of the restored image highly depends of knowledge of type and magnitude of noise. In the both methods spatial resolution of the restored images are improved, but much better in a case where autocorrelation functions of the noise and signal are used. This procedure is proposed as an objective pre-processing tool to put back imperfectness of mammography devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Multi-level methods and approximating distribution functions

Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie’s direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie’s direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146–179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Designing Cladded Components for High Temperature Nuclear Service: Part II—Design Rules

The challenge of using existing ASME Section III, Division 5, class A metallic materials for the construction of structural components of advanced reactors with corrosive coolants could be mitigated by allowing designers to use cladding to protect the base material from corrosion. However, the existing Section III, Division 5 rules provide no guidance on the evaluation of strain accumulation and creep-fatigue damage in cladded components. The availability of design rules for cladded components that do not require long-term clad material testing could promote the application of the cladding approach to accelerate the deployment schedule of these advanced reactor systems. To avoid long-term properties for the clad materials Part I of this work proposes two approximate design analysis methods for two types of clad materials—soft clads that creep much faster and have lower yield stress than the class A base material, and hard clads that creep much slower and have higher yield stress than the class A base material. The proposed analysis methods approximate the response of a soft clad by treating it as perfectly compliant and of a hard clad by treating it as linear elastic. Based on these approximate design analysis strategies this Part II develops a complete set of design rules for class A components cladded with either soft or hard clad materials. In conclusion, Part II discusses the reasoning behind the proposed design rules and uses example finite element analyses of representative reactor components to illustrate the use of these design methods.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

Expeditious modeling of vapor transport and reactions in polymeric materials

We present a methodology for approximating dynamic adsorption of vapor coupled with diffusion in polymeric materials. In previous publications, the dynamic adsorption was represented by ordinary differential equations (ODEs) and solved in concentration and parameter space. To accelerate the calculation, we have developed a statistical approximation method using computationally cheap surrogate models (e.g., algebraic polynomials) that replace the ODE solutions of adsorption and are coupled with the diffusion equations. Since the polynomial presentation of the adsorption term is obtained in a standard format prior to modeling coupled sorption‐diffusion, the adsorption operator can be expressed as input data in the transport code. Compared to conventional operator‐splitting methods, the polynomial approximation of adsorption offers better computational efficiency. The methodology is demonstrated and validated using a dynamic Langmuir adsorption model that is coupled to diffusion and absorption models and applied to a water vapor sorption‐diffusion process in polydimethylsiloxane polymers. © 2017 American Institute of Chemical Engineers AIChE J , 63: 4079–4089, 2017

Sun, Yunwei↗

DOE OSTI2022

Monitoring the propagation of mechanical discontinuity using data-driven causal discovery and supervised learning

Mechanical wave transmission through a material is influenced by the mechanical discontinuity in the material. The propagation of embedded discontinuities can be monitored by analyzing the wave-transmission measurements recorded by a multipoint sensor system placed on the surface of the material. The proposed workflow monitors the propagation of mechanical discontinuity through three stages, namely initial, intermediate, and final stages, by using supervised learning followed by data-driven causal discovery. To the end, the workflow processes the multipoint waveform measurements resulting from a single impulse source, while considering the effects of wave attenuation, dispersion and multiple wave-propagation modes due to the discontinuity and material boundaries. Among various feature reduction techniques ranging from decomposition methods to manifold approximation methods, the features derived based on statistical parameterizations of the measured waveforms lead to reliable monitoring that is robust to changes in precision, resolution, and signal-to-noise ratio of the multipoint sensor measurements. The numbers of zero-crossing, negative-turning, and positive turning in the waveforms are the strongest causal signatures of the propagation of mechanical discontinuity. Higher order moments of the waveforms, such as variance, skewness and kurtosis, are also strong causal signatures of the propagation. Finally, the newly discovered causal signatures confirm that the statistical correlations and conventional feature rankings are not always statistically significant indicators of causality.

42 ENGINEERING↗

DOE OSTI2020

Management of Risk and Uncertainty Through Optimized Co-Operation of Transmission Systems and Microgrids with Responsive Loads (Final Report)

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Management of Risk and Uncertainty Through Optimized Co-Operation of Transmission Systems and Microgrids With Responsive Loads (Final Report)

The evolution of the power system to the reliable, efficient and sustainable system of the future will involve development of both demand- and supply-side technology and operations. Ambitious national and state-level goals around the decarbonization of electricity relies on the integration of very high levels of renewable resources, most of which are variable and intermittent. The use of demand response is an ideal approach to counterbalance the intermittency of renewable generation and brings the consumer into the spotlight. Though individual consumers are interconnected at the low-voltage distribution system, these resources are typically modeled as variables at the transmission network level. Demand-side participation cannot be leveraged effectively without explicitly including the distribution system dynamics in the optimization-based wholesale market operations. This project grew from a vision for co-optimized interaction of distribution systems, or microgrids, with the high-voltage transmission system. In this framework, microgrids encompass consumers, distributed renewables and storage. The energy management system of the lower voltage system (distribution or microgrid) can also sell (buy) excess (necessary) energy from the transmission system. Until recently, very little research had been conducted on the co-optimization of these two systems due to computational limitations. However, advances in computational capabilities, and the judicious use of decomposition methods and innovative approximation methods for high-dimension dynamic programming made this goal a viable objective for this project, leading to a fundamental shift in the ability to integrate and fully utilize demand-side resources. To this end, the modeling framework developed introduces a novel co-optimization framework, to include the operations of both the transmission and distribution systems (or microgrids) in operational decision making. This framework was used to analyze renewable and distributed generation along with responsive demand and to compare the capability of co-optimized systems to perform with higher levels of variable renewables. An ideal microgrid is defined as an electric entity capable of operating in both interconnected (with the high-voltage grid) and islanded mode. As such, the microgrid should incorporate generating units (traditional units and intermittent) and if needed, exchange power with the high-voltage grid. The interplay between the microgrid and high-voltage grid motivated the development of the co-optimization approach to ensure efficient performance of the interconnected network. Results show that the use of a bi-level optimization approach is an appropriate structure, capable of co-optimizing a transmission system with multiple distribution systems and microgrids. While increasing the number of connected systems provides increasing flexibility for renewables integration this can also the economic benefits to the low-voltage subsystems with each additional system connected. Comparison of a traditional single-level decision structure with the co-optimization approach illustrates a reduction in overall system cost under co-optimization, while specific cost allocations to transmission and distribution systems are changed.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Optimizing lane reversals in transportation networks to reduce traffic congestion: A global optimization approach

This paper studies how to reduce the overall travel time of commuters in a transportation network by reversing the direction of some lanes in the network using a macroscopic network-wide perspective. Similar to the Network Design Problem, the lane reversal problem has been shown to be NP-hard given the dependence of the users’ route selection on the lane direction decision. Herein, we propose and compare three efficient methods to solve the routing and lane reversal problem jointly. First, we introduce an alternating method that decouples the routing and lane assignment problems. Second, we propose a Frank–Wolfe method that jointly takes gradient steps to adjust both the lane assignment and routing decisions. Third, we propose a convex approximation method that uses a threshold-based approach to convexify the joint routing and lane reversal objective. The convex approximation method is advantageous since it finds a global optimum solution for the approximated problem and it enables the possibility to include linear constraints. Using this method, we extend the main formulation to be able to limit a maximum number of reversed lanes, as well as to incorporate multiple origin–destination (OD) patterns. We test the proposed methods in a case study using the transportation network of Eastern Massachusetts where our results indicate an overall reduction in travel times of 4.7% by selecting the best 15 reversals. Moreover, using a small test network, we investigate the performance of the lane reversal strategies as a function of the OD demand symmetry. As expected, we observe that when the OD demand is very asymmetric (e.g., for a single OD pair, evacuations, large events), the reduction in travel times is larger than the symmetric case, reaching travel time reductions of 60%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

An extension of Thwaites’ method for turbulent boundary layers

Thwaites developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations. The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

17 WIND ENERGY↗

DOE OSTI2015

KAPPA: A PACKAGE FOR SYNTHESIS OF OPTICALLY THIN SPECTRA FOR THE NON-MAXWELLIAN κ-DISTRIBUTIONS BASED ON THE CHIANTI DATABASE

Non-Maxwellian κ-distributions have been detected in the solar transition region and in flares. These distributions are characterized by a high-energy tail and a near-Maxwellian core and are known to have a significant impact on the resulting optically thin spectra arising from collisionally dominated astrophysical plasmas. We developed the KAPPA package for the synthesis of such line and continuum spectra. The package is based on the freely available CHIANTI database and software, and can be used in a similar manner. Ionization and recombination rates together with the ionization equilibria are provided for a range of κ values. Distribution-averaged collision strengths for excitation are obtained using an approximate method for all transitions in all ions available within CHIANTI. The validity of this approximate method is tested through a comparison with direct calculations. Typical precisions of better than 5% are found with all cases being within 10%. Tools for the calculation of synthetic line and continuum intensities are provided and described. Examples of the synthetic spectra and SDO/AIA responses to emission for the κ-distributions are given.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Eulerian thermo-mechanical simulations of heterogeneous solid propellants using an approximate projection method

We present a mathematical model that describes thermo-mechanical deformations and thermal gradients on the unsteady burning of a heterogeneous solid propellant. A scaling study shows that the deformations in solid at combustion timescales can be treated as quasi-static. The resulting thermo-mechanical formulation is formulated on a Cartesian grid and makes use of a weak form of Chorin-type projection method to deal with large difference in shear modulus of constituent materials. Further, a one-dimensional verification study is carried out by comparing numerical simulations with those of an analytical model. In addition, convergence studies for a two-dimensional propellant sandwich configuration are presented for the stress, velocity, and reference map components. Finally, simulations are carried out for a two-dimensional random propellant pack and the time-averaged burn rate and strains are reported.

42 ENGINEERING↗

DOE OSTI2026

Solar and Storage Integration in the U.S. Southeast: Implications for Resource Adequacy [Slides]

In this study, we evaluate how an iterative portfolio approach compares to a more traditional capacity credit method, using the U.S. Southeast as a case study region. Using open-source planning and resource adequacy tools, we compare results using a capacity credit approximation method with those from iterating behind the two. We also explore how the iterative approach performs under a range of sensitivities, including higher load growth, regional coordination, and alternative weather years. We find that traditional capacity credit approximation methods can function well in today's system, but may face challenges for systems with higher levels of solar and storage. As such, integrating planning and resource adequacy models can address some of these gaps, helping planners deliver more reliable systems.

14 SOLAR ENERGY↗

DOE OSTI2021

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem

The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. Finally, we numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular meshes, where the method coincides with the $\mathbb{P}_1$ – $\mathbb{P}_0$ Scott-Vogelius scheme, and on square meshes, which are situations that are well-known to be unstable.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem

The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method (FEM) for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. We numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular and square meshes where the method coincides with the P 1 - P 0 Scott-Vogelius scheme, which is well-known to be unstable.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Mathematical Model for Li-S Cell with Shuttling-Induced Capacity Loss Approximation

Lithium sulfur (Li-S) batteries have the potential to outperform the current lithium ion batteries and transform the technology of the future. However, dissolution, diffusion, and shuttling of the dissolved polysulfides result in parasitic reactions and substantial capacity loss. To provide a better understanding of the shuttling process, a 1D porous electrode mathematical model has been developed in this paper. An approximation method is used to account for the shuttling-induced capacity loss by adding an extra source/sink term in the material balance equations for the species involved in the parasitic reactions. Shuttling constants used in the source terms can be determined by fitting the model predictions to the experimental measurements. Here, the results showed that by including the approximation method, the model was able to predict the active material loss and the continuous decrease of volume fractions of Li 2 S on the cathode surface. The model sheds light on the capacity loss mechanism occurring inside the cell as a result of the shuttling of polysulfides.

25 ENERGY STORAGE↗