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Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis (V.6.16 User's Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗

Representing ductile damage with the dual domain material point method

In this study, we incorporate a ductile damage material model into a computational framework based on the Dual Domain Material Point (DDMP) method. As an example, simulations of a flyer plate experiment involving ductile void growth and material failure are performed. The results are compared with experiments performed on high purity tantalum. We also compare the numerical results obtained from the DDMP method with those obtained from the traditional Material Point Method (MPM). Effects of an overstress model, artificial viscosity, and physical viscosity are investigated. Our results show that a physical bulk viscosity and overstress model are important in this impact and failure problem, while physical shear viscosity and artificial shock viscosity have negligible effects. A simple numerical procedure with guaranteed convergence is introduced to solve for the equilibrium plastic state from the ductile damage model.

36 MATERIALS SCIENCE↗

Evaluation of Automated Model Calibration Techniques for Residential Building Energy Simulation

This simulation study adapts and applies the general framework described in BESTEST-EX (Judkoff et al 2010) for self-testing residential building energy model calibration methods. BEopt/DOE-2.2 is used to evaluate four mathematical calibration methods in the context of monthly, daily, and hourly synthetic utility data for a 1960's-era existing home in a cooling-dominated climate. The home's model inputs are assigned probability distributions representing uncertainty ranges, random selections are made from the uncertainty ranges to define "explicit" input values, and synthetic utility billing data are generated using the explicit input values. The four calibration methods evaluated in this study are: an ASHRAE 1051-RP-based approach (Reddy and Maor 2006), a simplified simulated annealing optimization approach, a regression metamodeling optimization approach, and a simple output ratio calibration approach. The calibration methods are evaluated for monthly, daily, and hourly cases; various retrofit measures are applied to the calibrated models and the methods are evaluated based on the accuracy of predicted savings, computational cost, repeatability, automation, and ease of implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Nonrad: Computing nonradiative capture coefficients from first principles

Point defects in semiconductor crystals provide a means for carriers to recombine nonradiatively. This recombination process impacts the performance of devices. We present the Nonrad code that implements the first-principles approach of Alkauskas et al. (2014) [8] for the evaluation of nonradiative capture coefficients based on a quantum-mechanical description of the capture process. An approach for evaluating electron-phonon coupling within the projector augmented wave formalism is presented. We also show that the common procedure of replacing Dirac delta functions with Gaussians can introduce errors into the resulting capture rate, and implement an alternative scheme to properly account for vibrational broadening. Finally, we assess the accuracy of using an analytic approximation to the Sommerfeld parameter by comparing with direct numerical evaluation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion plus Selected Inversion

We describe how to apply the recently developed pole expansion plus selected inversion (PEpSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating charge density, total energy, Helmholtz free energy and atomic forces without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEpSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEpSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEpSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEpSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes on a single processor. We also show that the use of PEpSI does not lead to loss of accuracy required in a practical DFT calculation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

VALIDATION AND RESULTS OF A PSEUDO-MULTI-ZONE COMBUSTION TRAJECTORY PREDICTION MODEL FOR CAPTURING SOOT AND NOX FORMATION ON A MEDIUM DUTY DIESEL ENGINE

A pseudo-multi-zone phenomenological model has been created with the ultimate goal of supporting efforts to enable broader commercialization of low temperature combustion modes in diesel engines. The benefits of low temperature combustion are the simultaneous reduction in soot and nitric oxide emissions and increased engine efficiency if combustion is properly controlled. Determining what qualifies as low temperature combustion for any given engine can be difficult without expensive emissions analysis equipment. This determination can be made off-line using computer models or through factory calibration procedures. This process could potentially be simplified if a real-time prediction model could be implemented to run for any engine platform this is the motivation for this study. The major benefit of this model is the ability for it to predict the combustion trajectory, i.e. local temperature and equivalence ratio in the burning zones. The model successfully captures all the expected trends based on the experimental data and even highlights an opportunity for simply using the average reaction temperature and equivalence ratio as an indicator of emissions levels alone - without solving formation sub-models. This general type of modeling effort is not new, but a major effort was made to minimize the calculation duration to enable implementation as an input to real-time next-cycle engine controller Instead of simply using the predicted engine out soot and NOx levels, control decisions could be made based on the trajectory. This has the potential to save large amounts of calibration time because with minor tuning (the model has only one automatically determined constant) it is hoped that the control algorithm would be generally applicable.

Bittle, Joshua A.↗

SU-G-IeP3-05: Effects of Image Receptor Technology and Dose Reduction Software On Radiation Dose Estimates for Fluoroscopically-Guided Interventional (FGI) Procedures

Purpose: To investigate the effects of image receptor technology and dose reduction software on radiation dose estimates for most frequently performed fluoroscopically-guided interventional (FGI) procedures at a tertiary health care center. Methods: IRB approval was obtained for retrospective analysis of FGI procedures performed in the interventional radiology suites between January-2011 and December-2015. This included procedures performed using image-intensifier (II) based systems which were subsequently replaced, flat-panel-detector (FPD) based systems which were later upgraded with ClarityIQ dose reduction software (Philips Healthcare) and relatively new FPD system already equipped with ClarityIQ. Post procedure, technologists entered system-reported cumulative air kerma (CAK) and kerma-area product (KAP; only KAP for II based systems) in RIS; these values were analyzed. Data pre-processing included correcting typographical errors and cross-verifying CAK and KAP. The most frequent high and low dose FGI procedures were identified and corresponding CAK and KAP values were compared. Results: Out of 27,251 procedures within this time period, most frequent high and low dose procedures were chemo/immuno-embolization (n=1967) and abscess drainage (n=1821). Mean KAP for embolization and abscess drainage procedures were 260,657, 310,304 and 94,908 mGycm{sup 2}, and 14,497, 15,040 and 6307 mGycm{sup 2} using II-, FPD- and FPD with ClarityIQ- based systems, respectively. Statistically significant differences were observed in KAP values for embolization procedures with respect to different systems but for abscess drainage procedures significant differences were only noted between systems with FPD and FPD with ClarityIQ (p<0.05). Mean CAK reduced significantly from 823 to 308 mGy and from 43 to 21 mGy for embolization and abscess drainage procedures, respectively, in transitioning to FPD systems with ClarityIQ (p<0.05). Conclusion: While transitioning from II- to FPD- based systems was not associated with dose reduction for the most frequently performed FGI procedures, substantial dose reduction was noted with relatively newer systems and dose reduction software.

60 APPLIED LIFE SCIENCES↗

Computational Modeling of Fracture Toughness of Al-Si and Al-Zn-Mg-Cu Alloys with Detected Porosity

This article presents the results of an experimental and numerical analysis of the fracture resistance of cast aluminum alloys subjected to variable loads over time based on the fracture mechanics method. The subjects of the analysis were the AlSi9 and AlZn6MgCu alloys (usually used for plastic processing) in which the presence of porosities in the form of separate or dispersed voids was revealed experimentally. The material for the experimental procedures was obtained directly from a casting or from casting samples. Depending on the type of the defect detected, different numerical models were proposed. The results of the numerical calculations were verified experimentally. Static tensile tests, fatigue low-cycle tests, fracture mechanics tests, fatigue crack propagation tests, a microscopic examination of the sample fracture area, and an x-ray tomographic analysis were all performed. A correlation of the results between the numerical analysis and the experimental work has been found. On the basis of the proposed calculation models, the fatigue life of castings of the analyzed alloys can be predicted in the case of concentrated and dispersed defects.

36 MATERIALS SCIENCE↗

3D delivered dose assessment using a 4DCT-based motion model

Purpose: The purpose of this work is to develop a clinically feasible method of calculating actual delivered dose distributions for patients who have significant respiratory motion during the course of stereotactic body radiation therapy (SBRT). Methods: A novel approach was proposed to calculate the actual delivered dose distribution for SBRT lung treatment. This approach can be specified in three steps. (1) At the treatment planning stage, a patient-specific motion model is created from planning 4DCT data. This model assumes that the displacement vector field (DVF) of any respiratory motion deformation can be described as a linear combination of some basis DVFs. (2) During the treatment procedure, 2D time-varying projection images (either kV or MV projections) are acquired, from which time-varying “fluoroscopic” 3D images of the patient are reconstructed using the motion model. The DVF of each timepoint in the time-varying reconstruction is an optimized linear combination of basis DVFs such that the 2D projection of the 3D volume at this timepoint matches the projection image. (3) 3D dose distribution is computed for each timepoint in the set of 3D reconstructed fluoroscopic images, from which the total effective 3D delivered dose is calculated by accumulating deformed dose distributions. This approach was first validated using two modified digital extended cardio-torso (XCAT) phantoms with lung tumors and different respiratory motions. The estimated doses were compared to the dose that would be calculated for routine 4DCT-based planning and to the actual delivered dose that was calculated using “ground truth” XCAT phantoms at all timepoints. The approach was also tested using one set of patient data, which demonstrated the application of our method in a clinical scenario. Results: For the first XCAT phantom that has a mostly regular breathing pattern, the errors in 95% volume dose (D95) are 0.11% and 0.83%, respectively for 3D fluoroscopic images reconstructed from kV and MV projections compared to the ground truth, which is clinically comparable to 4DCT (0.093%). For the second XCAT phantom that has an irregular breathing pattern, the errors are 0.81% and 1.75% for kV and MV reconstructions, both of which are better than that of 4DCT (4.01%). In the case of real patient, although it is impossible to obtain the actual delivered dose, the dose estimation is clinically reasonable and demonstrates differences between 4DCT and MV reconstruction-based dose estimates. Conclusions: With the availability of kV or MV projection images, the proposed approach is able to assess delivered doses for all respiratory phases during treatment. Compared to the planning dose based on 4DCT, the dose estimation using reconstructed 3D fluoroscopic images was as good as 4DCT for regular respiratory pattern and was a better dose estimation for the irregular respiratory pattern.

60 APPLIED LIFE SCIENCES↗

Effective Ion Mobility Calculations for Macromolecules by Scattering off Electron Clouds

Broad commercialization and increasing resolving power of ion mobility spectrometry/mass spectrometry (IMS/MS) platforms has engendered an explosion of IMS applications to structural characterization of gas-phase biomolecules. That has renewed interest in more accurate and rapid ion mobility calculations needed to elicit ion geometries from the measurements. An approach based on scattering off electron density isosurfaces (SEDI) that mirrors the physics of molecular collisions was proven superior to the common methods involving atomic coordinates a decade ago, but has remained impractical for large ions because of extreme computational demands. Here, we accelerate SEDI by up to ~500 times using the fragment molecular orbital (FMO) approach for surface generation and the multiplexed scattering algorithm in conjunction with the new grid extrapolation procedure for cross section evaluations. Parallelization of the code on a supercomputer has produced major further speed gains, allowing SEDI calculations for proteins (defined by over a million surface points) with the precision of <0.1% in one minute. Initial tests reveal the anticipated dependences of mobility on the ion charge state and lower cross sections in view of reduced surface roughness. Present developments are expected to lead to broad application of SEDI in IMS studies of macromolecules, enabling more accurate and reliable structural assignments.

Alexeev, Yuri↗

Effects of anisotropic interaction-induced properties of hydrogen-rare gas compounds on rototranslational Raman scattering spectra: Comprehensive theoretical and numerical analysis

A comprehensive study is presented of many aspects of the depolarized anisotropic collision induced (CI) component of light scattered by weakly bound compounds composed of a dihydrogen molecule and a rare gas (Rg) atom, H{sub 2}–Rg. The work continues a series of earlier projects marking the revival of interest in linear light scattering following the development of new highly advanced tools of quantum chemistry and other theoretical, computational, and experimental means of spectral analyses. Sophisticated ab initio computing procedures are applied in order to obtain the anisotropic polarizability component’s dependence on the H{sub 2}–Rg geometry. These data are then used to evaluate the CI spectral lines for all types of Rg atoms ranging from He to Xe (Rn excluded). Evolution of the properties of CI spectra with growing polarizability/masses of the complexes studied is observed. Special attention is given to the heaviest, Kr and Xe based, scatterers. The influence of specific factors shaping the spectral lines (e.g., bound and metastable contribution, potential anisotropy) is discussed. Also the share of pressure broadened allowed rotational transitions in the overall spectral profile is taken into account and the extent to which it is separable from the pure CI contribution is discussed. We finish with a brief comparison between the obtained results and available experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Correlations of the Elemental Compositions of Primary Coal Tar and Char

We report that simulations of large-scale coal combustors rely on accurate submodels to describe the chemical and physical changes in coal during reaction. Typically, researchers use simplified empirical submodels tuned to experimental data to reduce the computational complexity. When data are not readily available, researchers use simplifying assumptions, which can create inaccuracies and biases in a large simulation. One such simplifying assumption in coal research is how to describe the elemental composition of primary pyrolysis products. This paper explores several different empirical model forms to predict the dry, ash-free fractions of C, H, O, N, and S in both the char and the tar, using variables such as parent coal composition, reaction conditions (temperatures and particle residence times), and key coal structural parameters derived from NMR measurements. These model forms were correlated to existing data using a wide range of experimental data using a cross-validation procedure. Since coal structural values can be expensive to measure, several correlations from the literature were used to estimate these values based on information from the proximate and ultimate analyses of the parent coal, including a new correlation for the coal aromaticity. These model forms were tested against a set of measured elemental compositions of tar and char to find the best fit to use in the cross-validation process. Lastly, the best empirical models are presented that predict elemental composition of the coal char and tar after devolatilization.

01 COAL, LIGNITE, AND PEAT↗

Variance-based sensitivity indices for stochastic models with correlated inputs

The goal of this article is the formulation of the principles of one of the possible strategies in implementing correlation between input random variables so as to be usable for algorithm development and the evaluation of Sobol’s sensitivity analysis. With regard to the types of stochastic computational models, which are commonly found in structural mechanics, an algorithm was designed for effective use in conjunction with Monte Carlo methods. Sensitivity indices are evaluated for all possible permutations of the decorrelation procedures for input parameters. The evaluation of Sobol’s sensitivity coefficients is illustrated on an example in which a computational model was used for the analysis of the resistance of a steel bar in tension with statistically dependent input geometric characteristics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Vector tomography for reconstructing electric fields with non-zero divergence in bounded domains

In vector tomography (VT), the aim is to reconstruct an unknown multi-dimensional vector field using line integral data. In the case of a 2-dimensional VT, two types of line integral data are usually required. These data correspond to integration of the parallel and perpendicular projection of the vector field along the integration lines and are called the longitudinal and transverse measurements, respectively. In most cases, however, the transverse measurements cannot be physically acquired. Therefore, the VT methods are typically used to reconstruct divergence-free (or source-free) velocity and flow fields that can be reconstructed solely from the longitudinal measurements. In this paper, we show how vector fields with non-zero divergence in a bounded domain can also be reconstructed from the longitudinal measurements without the need of explicitly evaluating the transverse measurements. To the best of our knowledge, VT has not previously been used for this purpose. In particular, we study low-frequency, time-harmonic electric fields generated by dipole sources in convex bounded domains which arise, for example, in electroencephalography (EEG) source imaging. We explain in detail the theoretical background, the derivation of the electric field inverse problem and the numerical approximation of the line integrals. We show that fields with non-zero divergence can be reconstructed from the longitudinal measurements with the help of two sparsity constraints that are constructed from the transverse measurements and the vector Laplace operator. As a comparison to EEG source imaging, we note that VT does not require mathematical modeling of the sources. By numerical simulations, we show that the pattern of the electric field can be correctly estimated using VT and the location of the source activity can be determined accurately from the reconstructed magnitudes of the field. - Highlights: • Vector tomography is used to reconstruct electric fields generated by dipole sources. • Inverse solutions are based on longitudinal and transverse line integral measurements. • Transverse line integral measurements are used as a sparsity constraint. • Numerical procedure to approximate the line integrals is described in detail. • Patterns of the studied electric fields are correctly estimated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗

Discrete Hahn polynomials for numerical solution of two-dimensional variable-order fractional Rayleigh–Stokes problem

The main aim of this paper is to find the numerical solutions of 2D Rayleigh–Stokes problem with the variable-order fractional derivatives in the Riemann–Liouville sense. The presented method is based on collocation procedure in combination with the new operational matrix of the variable-order fractional derivatives, in the Caputo sense, for the discrete Hahn polynomials. The main advantage of the proposed method is obtaining a global approximation for spatial and temporal discretizations, and it reduced the problem to an algebraic system, which is easier to solve. Also, the profit of approximating a continuous function by Hahn polynomials is that for computing the coefficients of the expansion, we only have to compute a summation and the calculation of coefficients is exact. The error bound for the approximate solution is estimated. Finally, we evaluate results of the presented method with other numerical methods.

97 MATHEMATICS AND COMPUTING↗

Multiscale Modeling of Hematologic Disorders

Parasitic infectious diseases and other hereditary hematologic disorders are often associated with major changes in the shape and viscoelastic properties of red blood cells (RBCs). Such changes can disrupt blood flow and even brain perfusion, as in the case of cerebral malaria. Modeling of these hematologic disorders requires a seamless multiscale approach, where blood cells and blood flow in the entire arterial tree are represented accurately using physiologically consistent parameters. In this chapter, we present a computational methodology based on dissipative particle dynamics (DPD) which models RBCs as well as whole blood in health and disease. DPD is a Lagrangian method that can be derived from systematic coarse-graining of molecular dynamics but can scale efficiently up to small arteries and can also be used to model RBCs down to spectrin level. To this end, we present two complementary mathematical models for RBCs and describe a systematic procedure on extracting the relevant input parameters from optical tweezers and microfluidic experiments for single RBCs. We then use these validated RBC models to predict the behavior of whole healthy blood and compare with experimental results. The same procedure is applied to modeling malaria, and results for infected single RBCs and whole blood are presented.

60 APPLIED LIFE SCIENCES↗

Use of C-Arm Cone Beam CT During Hepatic Radioembolization: Protocol Optimization for Extrahepatic Shunting and Parenchymal Enhancement

PurposeTo optimize a C-arm computed tomography (CT) protocol for radioembolization (RE), specifically for extrahepatic shunting and parenchymal enhancement.Materials and MethodsA prospective development study was performed per IDEAL recommendations. A literature-based protocol was applied in patients with unresectable and chemorefractory liver malignancies undergoing an angiography before radioembolization. Contrast and scan settings were adjusted stepwise and repeatedly reviewed in a consensus meeting. Afterwards, two independent raters analyzed all scans. A third rater evaluated the SPECT/CT scans as a reference standard for extrahepatic shunting and lack of target segment perfusion.ResultsFifty scans were obtained in 29 procedures. The first protocol, using a 6 s delay and 10 s scan, showed insufficient parenchymal enhancement. In the second protocol, the delay was determined by timing parenchymal enhancement on DSA power injection (median 8 s, range 4–10 s): enhancement improved, but breathing artifacts increased (from 0 to 27 %). Since the third protocol with a 5 s scan decremented subjective image quality, the second protocol was deemed optimal. Median CNR (range) was 1.7 (0.6–3.2), 2.2 (−1.4–4.0), and 2.1 (−0.3–3.0) for protocol 1, 2, and 3 (p = 0.80). Delineation of perfused segments was possible in 57, 73, and 44 % of scans (p = 0.13). In all C-arm CTs combined, the negative predictive value was 95 % for extrahepatic shunting and 83 % for lack of target segment perfusion.ConclusionAn optimized C-arm CT protocol was developed that can be used to detect extrahepatic shunts and non-perfusion of target segments during RE.

62 RADIOLOGY AND NUCLEAR MEDICINE↗