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DOE OSTI2016

Technical Note: Impact of the geometry dependence of the ion chamber detector response function on a convolution-based method to address the volume averaging effect

Purpose: To investigate the geometry dependence of the detector response function (DRF) of three commonly used scanning ionization chambers and its impact on a convolution-based method to address the volume averaging effect (VAE). Methods: A convolution-based approach has been proposed recently to address the ionization chamber VAE. It simulates the VAE in the treatment planning system (TPS) by iteratively convolving the calculated beam profiles with the DRF while optimizing the beam model. Since the convolved and the measured profiles are subject to the same VAE, the calculated profiles match the implicit “real” ones when the optimization converges. Three DRFs (Gaussian, Lorentzian, and parabolic function) were used for three ionization chambers (CC04, CC13, and SNC125c) in this study. Geometry dependent/independent DRFs were obtained by minimizing the difference between the ionization chamber-measured profiles and the diode-measured profiles convolved with the DRFs. These DRFs were used to obtain eighteen beam models for a commercial TPS. Accuracy of the beam models were evaluated by assessing the 20%–80% penumbra width difference (PWD) between the computed and diode-measured beam profiles. Results: The convolution-based approach was found to be effective for all three ionization chambers with significant improvement for all beam models. Up to 17% geometry dependence of the three DRFs was observed for the studied ionization chambers. With geometry dependent DRFs, the PWD was within 0.80 mm for the parabolic function and CC04 combination and within 0.50 mm for other combinations; with geometry independent DRFs, the PWD was within 1.00 mm for all cases. When using the Gaussian function as the DRF, accounting for geometry dependence led to marginal improvement (PWD < 0.20 mm) for CC04; the improvement ranged from 0.38 to 0.65 mm for CC13; for SNC125c, the improvement was slightly above 0.50 mm. Conclusions: Although all three DRFs were found adequate to represent the response of the studied ionization chambers, the Gaussian function was favored due to its superior overall performance. The geometry dependence of the DRFs can be significant for clinical applications involving small fields such as stereotactic radiotherapy.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Quantification of regional early stage gas exchange changes using hyperpolarized {sup 129}Xe MRI in a rat model of radiation-induced lung injury

Purpose: To assess the feasibility of hyperpolarized (HP) {sup 129}Xe MRI for detection of early stage radiation-induced lung injury (RILI) in a rat model involving unilateral irradiation by assessing differences in gas exchange dynamics between irradiated and unirradiated lungs. Methods: The dynamics of gas exchange between alveolar air space and pulmonary tissue (PT), PT and red blood cells (RBCs) was measured using single-shot spiral iterative decomposition of water and fat with echo asymmetry and least-squares estimation images of the right and left lungs of two age-matched cohorts of Sprague Dawley rats. The first cohort (n = 5) received 18 Gy irradiation to the right lung using a {sup 60}Co source and the second cohort (n = 5) was not irradiated and served as the healthy control. Both groups were imaged two weeks following irradiation when radiation pneumonitis (RP) was expected to be present. The gas exchange data were fit to a theoretical gas exchange model to extract measurements of pulmonary tissue thickness (L{sub PT}) and relative blood volume (V{sub RBC}) from each of the right and left lungs of both cohorts. Following imaging, lung specimens were retrieved and percent tissue area (PTA) was assessed histologically to confirm RP and correlate with MRI measurements. Results: Statistically significant differences in L{sub PT} and V{sub RBC} were observed between the irradiated and non-irradiated cohorts. In particular, L{sub PT} of the right and left lungs was increased approximately 8.2% and 5.0% respectively in the irradiated cohort. Additionally, V{sub RBC} of the right and left lungs was decreased approximately 36.1% and 11.7% respectively for the irradiated cohort compared to the non-irradiated cohort. PTA measurements in both right and left lungs were increased in the irradiated group compared to the non-irradiated cohort for both the left (P < 0.05) and right lungs (P < 0.01) confirming the presence of RP. PTA measurements also correlated with the MRI measurements for both the non-irradiated (r = 0.79, P < 0.01) and irradiated groups (r = 0.91, P < 0.01). Conclusions: Regional RILI can be detected two weeks post-irradiation using HP {sup 129}Xe MRI and analysis of gas exchange curves. This approach correlates well with histology and can potentially be used clinically to assess radiation pneumonitis associated with early RILI to improve radiation therapy outcomes.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Constructing stellarators with quasisymmetry to high order

Here, a method is given to rapidly compute quasisymmetric stellarator magnetic fields for plasma confinement, without the need to call a three-dimensional magnetohydrodynamic equilibrium code inside an optimization iteration. The method is based on direct solution of the equations of magnetohydrodynamic equilibrium and quasisymmetry using Garren & Boozer’s expansion about the magnetic axis ( Phys Fluids B, vol. 3, 1991, p. 2805), and it is several orders of magnitude faster than the conventional optimization approach. The work here extends the method of Landreman et al. ( J. Plasma Phys. , vol. 85, 2019, 905850103), which was limited to flux surfaces with elliptical cross-section, to higher order in the aspect-ratio expansion. As a result, configurations can be generated with strong shaping that achieve quasisymmetry to high accuracy. Using this construction, we give the first numerical demonstrations of Garren and Boozer’s ideal scaling of quasisymmetry breaking with the cube of the inverse aspect ratio. We also demonstrate a strongly non-axisymmetric configuration (vacuum rotational transform $\unicode[STIX]{x1D704} >0.4$ ) in which symmetry-breaking mode amplitudes throughout a finite volume are ${<}2\times 10^{-7}$ , the smallest ever reported. To generate boundary shapes of finite-minor-radius configurations, a careful analysis is given of the effect of substituting a finite minor radius into the near-axis expansion. In conclusion, the approach here can provide analytic insight into the space of possible quasisymmetric stellarator configurations, and it can be used to generate good initial conditions for conventional stellarator optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Evaluating interaction energies of weakly bonded systems using the Buckingham-Hirshfeld method

We present the finalized Buckingham-Hirshfeld method (BHD-DFT) for the evaluation of interaction energies of non-bonded dimers with Density Functional Theory (DFT). In the method, dispersion energies are evaluated from static multipole polarizabilities, obtained on-the-fly from Coupled Perturbed Kohn-Sham calculations and partitioned into diatomic contributions using the iterative Hirshfeld partitioning method. The dispersion energy expression is distributed over four atoms and has therefore a higher delocalized character compared to the standard pairwise expressions. Additionally, full multipolar polarizability tensors are used as opposed to effective polarizabilities, allowing to retain the anisotropic character at no additional computational cost. A density dependent damping function for the BLYP, PBE, BP86, B3LYP, and PBE0 functionals has been implemented, containing two global parameters which were fitted to interaction energies and geometries of a selected number of dimers using a bi-variate RMS fit. The method is benchmarked against the S22 and S66 data sets for equilibrium geometries and the S22x5 and S66x8 data sets for interaction energies around the equilibrium geometry. Best results are achieved using the B3LYP functional with mean average deviation values of 0.30 and 0.24 kcal/mol for the S22 and S66 data sets, respectively. This situates the BHD-DFT method among the best performing dispersion inclusive DFT methods. Effect of counterpoise correction on DFT energies is discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Few-view cone-beam CT reconstruction with deformed prior image

Purpose: Prior images can be incorporated into the image reconstruction process to improve the quality of subsequent cone-beam CT (CBCT) images from sparse-view or low-dose projections. The purpose of this work is to develop a deformed prior image-based reconstruction (DPIR) strategy to mitigate the deformation between the prior image and the target image. Methods: The deformed prior image is obtained by a projection-based registration approach. Specifically, the deformation vector fields used to deform the prior image are estimated through iteratively matching the forward projection of the deformed prior image and the measured on-treatment projections. The deformed prior image is then used as the prior image in the standard prior image constrained compressed sensing (PICCS) algorithm. A simulation study on an XCAT phantom and a clinical study on a head-and-neck cancer patient were conducted to evaluate the performance of the proposed DPIR strategy. Results: The deformed prior image matches the geometry of the on-treatment CBCT more closely as compared to the original prior image. Consequently, the performance of the DPIR strategy from few-view projections is improved in comparison to the standard PICCS algorithm, based on both visual inspection and quantitative measures. In the XCAT phantom study using 20 projections, the average root mean squared error is reduced from 14% in PICCS to 10% in DPIR, and the average universal quality index increases from 0.88 in PICCS to 0.92 in DPIR. Conclusions: The present DPIR approach provides a practical solution to the mismatch problem between the prior image and target image, which improves the performance of the original PICCS algorithm for CBCT reconstruction from few-view or low-dose projections.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-G-204-06: Correlation Between Texture Analysis-Based Model Observer and Human Observer in Diagnosis of Ischemic Infarct in Non-Contrast Head CT of Adults

Purpose: To investigate the correlation between texture analysis-based model observer and human observer in the task of diagnosis of ischemic infarct in non-contrast head CT of adults. Methods: Non-contrast head CTs of five patients (2 M, 3 F; 58–83 y) with ischemic infarcts were retro-reconstructed using FBP and Adaptive Statistical Iterative Reconstruction (ASIR) of various levels (10–100%). Six neuro -radiologists reviewed each image and scored image quality for diagnosing acute infarcts by a 9-point Likert scale in a blinded test. These scores were averaged across the observers to produce the average human observer responses. The chief neuro-radiologist placed multiple ROIs over the infarcts. These ROIs were entered into a texture analysis software package. Forty-two features per image, including 11 GLRL, 5 GLCM, 4 GLGM, 9 Laws, and 13 2-D features, were computed and averaged over the images per dataset. The Fisher-coefficient (ratio of between-class variance to in-class variance) was calculated for each feature to identify the most discriminating features from each matrix that separate the different confidence scores most efficiently. The 15 features with the highest Fisher -coefficient were entered into linear multivariate regression for iterative modeling. Results: Multivariate regression analysis resulted in the best prediction model of the confidence scores after three iterations (df=11, F=11.7, p-value<0.0001). The model predicted scores and human observers were highly correlated (R=0.88, R-sq=0.77). The root-mean-square and maximal residual were 0.21 and 0.44, respectively. The residual scatter plot appeared random, symmetric, and unbiased. Conclusion: For diagnosis of ischemic infarct in non-contrast head CT in adults, the predicted image quality scores from texture analysis-based model observer was highly correlated with that of human observers for various noise levels. Texture-based model observer can characterize image quality of low contrast, subtle texture changes in addition to human observers.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2022

The W4 method: A new multi-dimensional root-finding scheme for nonlinear systems of equations

We propose a new class of method for solving nonlinear systems of equations, which, among other things, has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extension to the Newton-Raphson (NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Radiative recombination data for tungsten ions: II. W{sup 47+}–W{sup 71+}

New radiative recombination and photoionization cross sections, radiative recombination rate coefficients, and radiated power loss rate coefficients are presented for 23 tungsten impurity ions in plasmas. We consider ions from W{sup 47+} to W{sup 71+} that are of importance to fusion studies for ITER and for experiments using electron beam ion traps. The calculations are fully relativistic and all significant multipoles of the radiative field are taken into account. The Dirac–Fock method is used to compute the electron wavefunctions. Radiative recombination rates and radiated power loss rates are found using the relativistic Maxwell–Jüttner distribution of the continuum electron velocity. The total radiative recombination cross sections are given in the electron energy range from 1 eV to ∼80keV. Partial cross sections for ground and excited states are approximated by an analytical expression involving five fit parameters. Radiative recombination rates and radiated power loss rates are calculated in the temperature range from 10{sup 4}K to 10{sup 9}K. The total radiative recombination rates are approximated by another analytical expression with four fit parameters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2014

High-speed adaptive contact-mode atomic force microscopy imaging with near-minimum-force

In this paper, an adaptive contact-mode imaging approach is proposed to replace the traditional contact-mode imaging by addressing the major concerns in both the speed and the force exerted to the sample. The speed of the traditional contact-mode imaging is largely limited by the need to maintain precision tracking of the sample topography over the entire imaged sample surface, while large image distortion and excessive probe-sample interaction force occur during high-speed imaging. In this work, first, the image distortion caused by the topography tracking error is accounted for in the topography quantification. Second, the quantified sample topography is utilized in a gradient-based optimization method to adjust the cantilever deflection set-point for each scanline closely around the minimal level needed for maintaining stable probe-sample contact, and a data-driven iterative feedforward control that utilizes a prediction of the next-line topography is integrated to the topography feeedback loop to enhance the sample topography tracking. The proposed approach is demonstrated and evaluated through imaging a calibration sample of square pitches at both high speeds (e.g., scan rate of 75 Hz and 130 Hz) and large sizes (e.g., scan size of 30 μm and 80 μm). The experimental results show that compared to the traditional constant-force contact-mode imaging, the imaging speed can be increased by over 30 folds (with the scanning speed at 13 mm/s), and the probe-sample interaction force can be reduced by more than 15% while maintaining the same image quality.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater–Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimated experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Subcritical Multiplication with a Fixed Source

In a subcritical, multiplying medium, the system multiplication describes the expected total number of neutrons created by a single source neutron. Subcriticality plays a large role in criticality safety and thus it is vital for the subcritical multiplication factor be accurate, especially as a system approaches criticality. This work examines the accuracy of calculating the system multiplication using the MCNP6.2 ® k-eigenvalue power iteration (KCODE) method when a fixed-point source is present in a multiplying medium, for near critical systems. This work compares the standard approach for calculating system multiplication, using the fixed-source calculational approach, to a new, single k-eigenvalue power iteration approach that incorporates a fixed-source component and a fission-source component into a single calculation. For the remainder of this paper, some theoretical background and numerical results for an approximate k eigenvalue approach, an accurate fixed-source approach and a new and more accurate k-eigenvalue approach to computing system multiplication are provided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Dynamic flux surrogate-based partitioned methods for interface problems

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. In conclusion, we provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.

Dynamic mode decomposition (DMD)↗

DOE OSTI2016

SU-F-J-218: Predicting Radiation-Induced Xerostomia by Dosimetrically Accounting for Daily Setup Uncertainty During Head and Neck IMRT

Purpose: To determine if the accumulated parotid dosimetry using planning CT to daily CBCT deformation and dose re-calculation can predict for radiation-induced xerostomia. Methods: To track and dosimetrically account for the effects of anatomical changes on the parotid glands, we propagated physicians’ contours from planning CT to daily CBCT using a deformable registration with iterative CBCT intensity correction. A surface mesh for each OAR was created with the deformation applied to the mesh to obtain the deformed parotid volumes. Daily dose was computed on the deformed CT and accumulated to the last fraction. For both the accumulated and the planned parotid dosimetry, we tested the prediction power of different dosimetric parameters including D90, D50, D10, mean, standard deviation, min/max dose to the combined parotids and patient age to severe xerostomia (NCI-CTCAE grade≥2 at 6 mo follow-up). We also tested the dosimetry to parotid sub-volumes. Three classification algorithms, random tree, support vector machine, and logistic regression were tested to predict severe xerostomia using a leave-one-out validation approach. Results: We tested our prediction model on 35 HN IMRT cases. Parameters from the accumulated dosimetry model demonstrated an 89% accuracy for predicting severe xerostomia. Compared to the planning dosimetry, the accumulated dose consistently demonstrated higher prediction power with all three classification algorithms, including 11%, 5% and 30% higher accuracy, sensitivity and specificity, respectively. Geometric division of the combined parotid glands into superior-inferior regions demonstrated ∼5% increased accuracy than the whole volume. The most influential ranked features include age, mean accumulated dose of the submandibular glands and the accumulated D90 of the superior parotid glands. Conclusion: We demonstrated that the accumulated parotid dosimetry using CT-CBCT registration and dose re-calculation more accurately predicts for severe xerostomia and that the superior portion of the parotid glands may be particularly important in predicting for severe xerostomia. This work was supported in part by NIH/NCI under grant R42CA137886 and in part by Toshiba big data research project funds.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

SU-E-P-49: Evaluation of Image Quality and Radiation Dose of Various Unenhanced Head CT Protocols

Purpose: To evaluate the diagnostic value of various unenhanced head CT protocols and predicate acceptable radiation dose level for head CT exam. Methods: Our retrospective analysis included 3 groups, 20 patients per group, who underwent clinical routine unenhanced adult head CT examination. All exams were performed axially with 120 kVp. Three protocols, 380 mAs without iterative reconstruction and automAs, 340 mAs with iterative reconstruction without automAs, 340 mAs with iterative reconstruction and automAs, were applied on each group patients respectively. The images were reconstructed with H30, J30 for brain window and H60, J70 for bone window. Images acquired with three protocols were randomized and blindly reviewed by three radiologists. A 5 point scale was used to rate each exam The percentage of exam score above 3 and average scores of each protocol were calculated for each reviewer and tissue types. Results: For protocols without automAs, the average scores of bone window with iterative reconstruction were higher than those without iterative reconstruction for each reviewer although the radiation dose was 10 percentage lower. 100 percentage exams were scored 3 or higher and the average scores were above 4 for both brain and bone reconstructions. The CTDIvols are 64.4 and 57.8 mGy of 380 and 340 mAs, respectively. With automAs, the radiation dose varied with head size, resulting in 47.5 mGy average CTDIvol between 39.5 and 56.5 mGy. 93 and 98 percentage exams were scored great than 3 for brain and bone windows, respectively. The diagnostic confidence level and image quality of exams with AutomAs were less than those without AutomAs for each reviewer. Conclusion: According to these results, the mAs was reduced to 300 with automAs OFF for head CT exam. The radiation dose was 20 percentage lower than the original protocol and the CTDIvol was reduced to 51.2 mGy.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

SU-F-J-105: Towards a Novel Treatment Planning Pipeline Delivering Pareto- Optimal Plans While Enabling Inter- and Intrafraction Plan Adaptation

Purpose: To develop a new IMRT treatment planning methodology suitable for the new generation of MR-linear accelerator machines. The pipeline is able to deliver Pareto-optimal plans and can be utilized for conventional treatments as well as for inter- and intrafraction plan adaptation based on real-time MR-data. Methods: A Pareto-optimal plan is generated using the automated multicriterial optimization approach Erasmus-iCycle. The resulting dose distribution is used as input to the second part of the pipeline, an iterative process which generates deliverable segments that target the latest anatomical state and gradually converges to the prescribed dose. This process continues until a certain percentage of the dose has been delivered. Under a conventional treatment, a Segment Weight Optimization (SWO) is then performed to ensure convergence to the prescribed dose. In the case of inter- and intrafraction adaptation, post-processing steps like SWO cannot be employed due to the changing anatomy. This is instead addressed by transferring the missing/excess dose to the input of the subsequent fraction. In this work, the resulting plans were delivered on a Delta4 phantom as a final Quality Assurance test. Results: A conventional static SWO IMRT plan was generated for two prostate cases. The sequencer faithfully reproduced the input dose for all volumes of interest. For the two cases the mean relative dose difference of the PTV between the ideal input and sequenced dose was 0.1% and −0.02% respectively. Both plans were delivered on a Delta4 phantom and passed the clinical Quality Assurance procedures by achieving 100% pass rate at a 3%/3mm gamma analysis. Conclusion: We have developed a new sequencing methodology capable of online plan adaptation. In this work, we extended the pipeline to support Pareto-optimal input and clinically validated that it can accurately achieve these ideal distributions, while its flexible design enables inter- and intrafraction plan adaptation. This research is financially supported by Elekta AB, Stockholm, Sweden.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

WE-DE-BRA-09: Fast Megavoltage CT Imaging with Rapid Scan Time and Low Imaging Dose in Helical Tomotherapy

Purpose: Megavoltage computed tomography (MVCT) imaging has been widely used for daily patient setup with helical tomotherapy (HT). One drawback of MVCT is its very long imaging time, owing to slow couch speed. The purpose of this study was to develop an MVCT imaging method allowing faster couch speeds, and to assess its accuracy for image guidance for HT. Methods: Three cadavers (mimicking closest physiological and physical system of patients) were scanned four times with couch speeds of 1, 2, 3, and 4 mm/s. The resulting MVCT images were reconstructed using an iterative reconstruction (IR) algorithm. The MVCT images were registered with kilovoltage CT images, and the registration errors were compared with the errors with conventional filtered back projection (FBP) algorithm. Moreover, the fast MVCT imaging was tested in three cases of total marrow irradiation as a clinical trial. Results: Three-dimensional registration errors of the MVCT images reconstructed with the IR algorithm were significantly smaller (p < 0.05) than the errors of images reconstructed with the FBP algorithm at fast couch speeds (3, 4 mm/s). The scan time and imaging dose at a speed of 4 mm/s were reduced to 30% of those from a conventional coarse mode scan. For the patient imaging, a limited number of conventional MVCT (1.2 mm/s) and fast MVCT (3 mm/s) reveals acceptable reduced imaging time and dose able to use for anatomical registration. Conclusion: Fast MVCT with IR algorithm maybe clinically feasible alternative for rapid 3D patient localization. This technique may also be useful for calculating daily dose distributions or organ motion analyses in HT treatment over a wide area.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

Adaptive Mixed GMsFEM for Flows in Heterogeneous Media

Abstract In this paper, we present two adaptive methods for the basis enrichment of the mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving the flow problem in heterogeneous media. We develop an a-posteriori error indicator which depends on the norm of a local residual operator. Based on this indicator, we construct an offline adaptive method to increase the number of basis functions locally in coarse regions with large local residuals. We also develop an online adaptive method which iteratively enriches the function space by adding new functions computed based on the residual of the previous solution and special minimum energy snapshots. We show theoretically and numerically the convergence of the two methods. The online method is, in general, better than the offline method as the online method is able to capture distant effects (at a cost of online computations), and both methods have faster convergence than a uniform enrichment. Analysis shows that the online method should start with a certain number of initial basis functions in order to have the best performance. The numerical results confirm this and show further that with correct selection of initial basis functions, the convergence of the online method can be independent of the contrast of the medium. We consider cases with both very high and very low conducting inclusions and channels in our numerical experiments.

Mathematics↗

DOE OSTI2016

The moisture outgassing kinetics of a silica reinforced polydimethylsiloxane

We investigated a silica-filled polydimethylsiloxane (PDMS) composite M9787 for potential outgassing in a vacuum/dry environment with the temperature programmed desorption/reaction method. The outgassing kinetics of 463 K vacuum heat-treated samples, vacuum heat-treated samples which were subsequently re-exposed to moisture, and untreated samples were extracted using the isoconversional and constrained iterative regression methods in a complementary fashion. Density functional theory (DFT) calculations of water interactions with a silica surface were also performed to provide insight into the structural motifs leading to the obtained kinetic parameters. Kinetic analysis/model revealed that no outgassing occurs from the vacuum heat-treated samples in subsequent vacuum/dry environment applications at room temperature (~300 K). Moreover, the main effect of re-exposure of the vacuum heat-treated samples to a glove box condition (~30 ppm by volume of H 2 O) for even a couple of days was the formation, on the silica surface fillers, of ~60 ppm by weight of physisorbed and loosely bonded moisture, which subsequently outgasses at room temperature in a vacuum/dry environment in a time span of 10 yr. However, without any vacuum heat treatment and even after 1 h of vacuum pump down, about 300 ppm by weight of H 2 O would be released from the PDMS in the next few hours. Thereafter the outgassing rate slows down substantially. Our presented methodology of using the isoconversional kinetic analysis results and some appropriate nature of the reaction as the constraints for more accurate iterative regression analysis/deconvolution of complex kinetic spectra, and of checking the so-obtained results with first principle calculations such as DFT can serve as a template for treating other complex physical/chemical processes as well.

36 MATERIALS SCIENCE↗