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Results for “total variation regularization”

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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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Cardiac C-arm computed tomography using a 3D + time ROI reconstruction method with spatial and temporal regularization

Purpose: Reconstruction of the beating heart in 3D + time in the catheter laboratory using only the available C-arm system would improve diagnosis, guidance, device sizing, and outcome control for intracardiac interventions, e.g., electrophysiology, valvular disease treatment, structural or congenital heart disease. To obtain such a reconstruction, the patient's electrocardiogram (ECG) must be recorded during the acquisition and used in the reconstruction. In this paper, the authors present a 4D reconstruction method aiming to reconstruct the heart from a single sweep 10 s acquisition. Methods: The authors introduce the 4D RecOnstructiOn using Spatial and TEmporal Regularization (short 4D ROOSTER) method, which reconstructs all cardiac phases at once, as a 3D + time volume. The algorithm alternates between a reconstruction step based on conjugate gradient and four regularization steps: enforcing positivity, averaging along time outside a motion mask that contains the heart and vessels, 3D spatial total variation minimization, and 1D temporal total variation minimization. Results: 4D ROOSTER recovers the different temporal representations of a moving Shepp and Logan phantom, and outperforms both ECG-gated simultaneous algebraic reconstruction technique and prior image constrained compressed sensing on a clinical case. It generates 3D + time reconstructions with sharp edges which can be used, for example, to estimate the patient's left ventricular ejection fraction. Conclusions: 4D ROOSTER can be applied for human cardiac C-arm CT, and potentially in other dynamic tomography areas. It can easily be adapted to other problems as regularization is decoupled from projection and back projection.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2025

A Variational Autoencoder Model Toward Molecular Structure Representation Learning of Fuels

Here, in this work, a Variational Autoencoder (VAE)-based data-driven modeling framework is developed with the overarching goal of enabling fuel design. The VAE model is trained on a large dataset with several chemical species to learn a compressed latent space molecular representation. Chemical structure in the form of Simplified Molecular Input Line Entry System (SMILES) string is fed as input, encoded into the VAE latent space, and decoded back to the SMILES string using Long Short-Term Memory (LSTM) networks. Complexities of the VAE training loss function are thoroughly examined by varying the weightage (beta (𝜷) parameter) of the latent space regularization term, thereby assessing the balance between reconstruction accuracy and validity, and focusing on both accurate molecular structure reconstruction and latent space consistency. Two different strategies for 𝜷 variation are evaluated: linear annealing and cyclic annealing. In addition, the impact of total correlation adjustment and hierarchical priors is also studied with regard to the balance between reconstruction fidelity and latent space regularization, and potential issues such as posterior collapse, over-regularization, and poor disentanglement of latent variables. Overall, the best performance of the model is achieved with hierarchical priors and incrementally increasing 𝜷 from 0 to a threshold value of 0.25 over 75 epochs. The generative VAE model can be readily coupled with Quantitative Structure–Property Relationship (QSPR) analysis to develop an integrated end-to-end framework for fuel-property prediction and molecular design of novel promising fuels.

fuel design↗
DOE OSTI2022

Using ultrasonic attenuation in cortical bone to infer distributions on pore size

Here, in this work we infer the underlying distribution on pore radius in human cortical bone samples using ultrasonic attenuation data. We first discuss how to formulate polydisperse attenuation models using a probabilistic approach and the Waterman Truell model for scattering attenuation. We then compare the Independent Scattering Approximation and the higher-order Waterman Truell models’ forward predictions for total attenuation in polydisperse samples. Following this, we formulate an inverse problem under the Prohorov Metric Framework coupled with variational regularization to stabilize this inverse problem. We then use experimental attenuation data taken from human cadaver samples and solve inverse problems resulting in nonparametric estimates of the probability density function on pore radius. We compare these estimates to the “true” microstructure of the bone samples determined via microCT imaging. We find that our methodology allows us to reliably estimate the underlying microstructure of the bone from attenuation data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

TH-E-17A-02: High-Pitch and Sparse-View Helical 4D CT Via Iterative Image Reconstruction Method Based On Tensor Framelet

Purpose: 4D CT is routinely performed during radiation therapy treatment planning of thoracic and abdominal cancers. Compared with the cine mode, the helical mode is advantageous in temporal resolution. However, a low pitch (∼0.1) for 4D CT imaging is often required instead of the standard pitch (∼1) for static imaging, since standard image reconstruction based on analytic method requires the low-pitch scanning in order to satisfy the data sufficient condition when reconstructing each temporal frame individually. In comparison, the flexible iterative method enables the reconstruction of all temporal frames simultaneously, so that the image similarity among frames can be utilized to possibly perform high-pitch and sparse-view helical 4D CT imaging. The purpose of this work is to investigate such an exciting possibility for faster imaging with lower dose. Methods: A key for highpitch and sparse-view helical 4D CT imaging is the simultaneous reconstruction of all temporal frames using the prior that temporal frames are continuous along the temporal direction. In this work, such a prior is regularized through the sparsity transform based on spatiotemporal tensor framelet (TF) as a multilevel and high-order extension of total variation transform. Moreover, GPU-based fast parallel computing of X-ray transform and its adjoint together with split Bregman method is utilized for solving the 4D image reconstruction problem efficiently and accurately. Results: The simulation studies based on 4D NCAT phantoms were performed with various pitches (i.e., 0.1, 0.2, 0.5, and 1) and sparse views (i.e., 400 views per rotation instead of standard >2000 views per rotation), using 3D iterative individual reconstruction method based on 3D TF and 4D iterative simultaneous reconstruction method based on 4D TF respectively. Conclusion: The proposed TF-based simultaneous 4D image reconstruction method enables high-pitch and sparse-view helical 4D CT with lower dose and faster speed.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗
DOE OSTI2024

Rapid Optimization of Total Variation with Applications in Imaging, Additive Manufacturing, and Qualification

Total Variation optimization penalizes the gradient of a control variable or state. While this work focuses on image processing in particular, it has also found applications in inverse problems and topology optimization. In image processing, the goal is to maintain faithfulness to the original image while denoising and/or deblurring. Additionally, bilevel optimization over the spatially varying regularization weights can illuminate interfaces such as damage regions and other anomalies. We will address two fundamental challenges with TV-optimization: (i) the typical slow convergence of existing TV-optimization methods, and (ii) the selection of spatially varying TV parameters to promote interface detection. Additionally, we will apply such techniques to image data collected in additive manufacturing. In said context, stochasticity in build events induces flaws in the manufactured piece, compromising the integrity of said part. There is a critical need for in-situ monitoring to spot anomalies once they form, and in this setting we apply our total variation and hyperparameter solvers. We will develop a customized algorithm based on for extreme-scale TV-optimization that achieves super-linear or quadratic-convergence, a critical property for real-time, image-by-image analysis. A worst-case outcome is a preprocessing step that enhances image quality in-situ, specifically for out-of-focus and noisy images.

36 MATERIALS SCIENCE↗
DOE OSTI2016

MO-DE-207A-08: Four-Dimensional Cone-Beam CT Iterative Reconstruction with Time-Ordered Chain Graph Model for Non-Periodic Organ Motion and Deformation

Purpose: The purpose of this study is to propose a new concept of four-dimensional (4D) cone-beam CT (CBCT) reconstruction for non-periodic organ motion using the Time-ordered Chain Graph Model (TCGM), and to compare the reconstructed results with the previously proposed methods, the total variation-based compressed sensing (TVCS) and prior-image constrained compressed sensing (PICCS). Methods: CBCT reconstruction method introduced in this study consisted of maximum a posteriori (MAP) iterative reconstruction combined with a regularization term derived from a concept of TCGM, which includes a constraint coming from the images of neighbouring time-phases. The time-ordered image series were concurrently reconstructed in the MAP iterative reconstruction framework. Angular range of projections for each time-phase was 90 degrees for TCGM and PICCS, and 200 degrees for TVCS. Two kinds of projection data, an elliptic-cylindrical digital phantom data and two clinical patients’ data, were used for reconstruction. The digital phantom contained an air sphere moving 3 cm along longitudinal axis, and temporal resolution of each method was evaluated by measuring the penumbral width of reconstructed moving air sphere. The clinical feasibility of non-periodic time-ordered 4D CBCT reconstruction was also examined using projection data of prostate cancer patients. Results: The results of reconstructed digital phantom shows that the penumbral widths of TCGM yielded the narrowest result; PICCS and TCGM were 10.6% and 17.4% narrower than that of TVCS, respectively. This suggests that the TCGM has the better temporal resolution than the others. Patients’ CBCT projection data were also reconstructed and all three reconstructed results showed motion of rectal gas and stool. The result of TCGM provided visually clearer and less blurring images. Conclusion: The present study demonstrates that the new concept for 4D CBCT reconstruction, TCGM, combined with MAP iterative reconstruction framework enables time-ordered image reconstruction with narrower time-window.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Fast and low-dose computed laminography using compressive sensing based technique

Computed laminography (CL) is well known for inspecting microstructures in the materials, weldments and soldering defects in high density packed components or multilayer printed circuit boards. The overload problem on x-ray tube and gross failure of the radio-sensitive electronics devices during a scan are among important issues in CL which needs to be addressed. The sparse-view CL can be one of the viable option to overcome such issues. In this work a numerical aluminum welding phantom was simulated to collect sparsely sampled projection data at only 40 views using a conventional CL scanning scheme i.e. oblique scan. A compressive-sensing inspired total-variation (TV) minimization algorithm was utilized to reconstruct the images. It is found that the images reconstructed using sparse view data are visually comparable with the images reconstructed using full scan data set i.e. at 360 views on regular interval. We have quantitatively confirmed that tiny structures such as copper and tungsten slags, and copper flakes in the reconstructed images from sparsely sampled data are comparable with the corresponding structure present in the fully sampled data case. A blurring effect can be seen near the edges of few pores at the bottom of the reconstructed images from sparsely sampled data, despite the overall image quality is reasonable for fast and low-dose NDT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

TU-CD-BRA-12: Coupling PET Image Restoration and Segmentation Using Variational Method with Multiple Regularizations

Purpose: To propose a new variational method which couples image restoration with tumor segmentation for PET images using multiple regularizations. Methods: Partial volume effect (PVE) is a major degrading factor impacting tumor segmentation accuracy in PET imaging. The existing segmentation methods usually need to take prior calibrations to compensate PVE and they are highly system-dependent. Taking into account that image restoration and segmentation can promote each other and they are tightly coupled, we proposed a variational method to solve the two problems together. Our method integrated total variation (TV) semi-blind deconvolution and Mumford-Shah (MS) segmentation. The TV norm was used on edges to protect the edge information, and the L{sub 2} norm was used to avoid staircase effect in the no-edge area. The blur kernel was constrained to the Gaussian model parameterized by its variance and we assumed that the variances in the X-Y and Z directions are different. The energy functional was iteratively optimized by an alternate minimization algorithm. Segmentation performance was tested on eleven patients with non-Hodgkin’s lymphoma, and evaluated by Dice similarity index (DSI) and classification error (CE). For comparison, seven other widely used methods were also tested and evaluated. Results: The combination of TV and L{sub 2} regularizations effectively improved the segmentation accuracy. The average DSI increased by around 0.1 than using either the TV or the L{sub 2} norm. The proposed method was obviously superior to other tested methods. It has an average DSI and CE of 0.80 and 0.41, while the FCM method — the second best one — has only an average DSI and CE of 0.66 and 0.64. Conclusion: Coupling image restoration and segmentation can handle PVE and thus improves tumor segmentation accuracy in PET. Alternate use of TV and L2 regularizations can further improve the performance of the algorithm. This work was supported in part by National Natural Science Foundation of China (NNSFC), under Grant No.61375018, and Fundamental Research Funds for the Central Universities, under Grant No. 2012QN086. Wei Lu was supported in part by the National Institutes of Health (NIH) Grant No. R01 CA172638.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Characterization of Inclusions in 3rd Generation Advanced High-Strength Steels

Samples taken from laboratory-produced 3rd generation advanced high-strength steels, solidified at a low cooling rate, have been investigated to study the characteristics of non-metallic inclusions. Two steels, containing 2 and 5 pct Mn content, were produced for this purpose. A higher number of total inclusions were observed in 5 pct Mn steel. The four main types of inclusions observed were Al{sub 2}O{sub 3}, AlN, MnS, and AlSiMn-oxide. These classes were divided into subclasses according to variations in their chemistry. The major subclasses of AlN inclusions are either plate-like or regular in shape and have different size distributions. Thermodynamic calculations suggest that plate-like AlN inclusions are formed at the initial stage of solidification, while faceted/regular-shaped inclusions are precipitated toward the end of solidification. Moreover, it was found that the size of nitride inclusions is related to their N content. This phenomenon is discussed from the viewpoint of nucleation theory.

36 MATERIALS SCIENCE↗
DOE OSTI2014

WE-B-19A-01: SRT II: Uncertainties in SRT

SRS delivery has undergone major technical changes in the last decade, transitioning from predominantly frame-based treatment delivery to imageguided, frameless SRS. It is important for medical physicists working in SRS to understand the magnitude and sources of uncertainty involved in delivering SRS treatments for a multitude of technologies (Gamma Knife, CyberKnife, linac-based SRS and protons). Sources of SRS planning and delivery uncertainty include dose calculation, dose fusion, and intra- and inter-fraction motion. Dose calculations for small fields are particularly difficult because of the lack of electronic equilibrium and greater effect of inhomogeneities within and near the PTV. Going frameless introduces greater setup uncertainties that allows for potentially increased intra- and interfraction motion, The increased use of multiple imaging modalities to determine the tumor volume, necessitates (deformable) image and contour fusion, and the resulting uncertainties introduced in the image registration process further contribute to overall treatment planning uncertainties. Each of these uncertainties must be quantified and their impact on treatment delivery accuracy understood. If necessary, the uncertainties may then be accounted for during treatment planning either through techniques to make the uncertainty explicit, or by the appropriate addition of PTV margins. Further complicating matters, the statistics of 1-5 fraction SRS treatments differ from traditional margin recipes relying on Poisson statistics. In this session, we will discuss uncertainties introduced during each step of the SRS treatment planning and delivery process and present margin recipes to appropriately account for such uncertainties. Learning Objectives: To understand the major contributors to the total delivery uncertainty in SRS for Gamma Knife, CyberKnife, and linac-based SRS. Learn the various uncertainties introduced by image fusion, deformable image registration, and contouring variation. Learn a variety of strategies for dealing with uncertainty, including margin recipes and explicit visualization of uncertainty. Understand how the assessment of PTV margins differs from regular fractionation (van Herk recipe) for 1–5 fraction deliveries.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Sparsity-based acoustic inversion in cross-sectional multiscale optoacoustic imaging

Purpose: With recent advancement in hardware of optoacoustic imaging systems, highly detailed cross-sectional images may be acquired at a single laser shot, thus eliminating motion artifacts. Nonetheless, other sources of artifacts remain due to signal distortion or out-of-plane signals. The purpose of image reconstruction algorithms is to obtain the most accurate images from noisy, distorted projection data. Methods: In this paper, the authors use the model-based approach for acoustic inversion, combined with a sparsity-based inversion procedure. Specifically, a cost function is used that includes the L1 norm of the image in sparse representation and a total variation (TV) term. The optimization problem is solved by a numerically efficient implementation of a nonlinear gradient descent algorithm. TV–L1 model-based inversion is tested in the cross section geometry for numerically generated data as well as for in vivo experimental data from an adult mouse. Results: In all cases, model-based TV–L1 inversion showed a better performance over the conventional Tikhonov regularization, TV inversion, and L1 inversion. In the numerical examples, the images reconstructed with TV–L1 inversion were quantitatively more similar to the originating images. In the experimental examples, TV–L1 inversion yielded sharper images and weaker streak artifact. Conclusions: The results herein show that TV–L1 inversion is capable of improving the quality of highly detailed, multiscale optoacoustic images obtained in vivo using cross-sectional imaging systems. As a result of its high fidelity, model-based TV–L1 inversion may be considered as the new standard for image reconstruction in cross-sectional imaging.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Compressed Streak Imaging Beam Diagnostic

We are planning a new beam diagnostic based on Compressed Ultrafast Photography (CUP)1.A foil inserted in the beam path is used to generate a continuous optical image of the beam, which is the same technique used on the existing DARHT II beam imaging diagnostic. This existing diagnostic compresses the beam image with anamorphic lenses into four views that are streaked simultaneously on two streak cameras. In our new beam diagnostic design the anamorphic lenses are replaced with regular lenses and the beam image is stamped with a pseudo-random mask pattern. The full image is imaged onto a streak camera with its entrance slit expanded. Modifying the CUP technique, which uses a single streaked image, our design splits the image into four rotated copies and puts all four images on two streak cameras. A data cube of multiple image frames is reconstructed from the streak camera data through the use of the TwiST algorithm2 combined with total variation denoising3. The additional rotated images improve spatial resolution and reduce noise and image artifacts compared to using a single streaked image. In reconstructions of simulated data, fine detail in the beam profile can be seen and there is a remarkable absence of image artifacts compared to the existing DARHT II beam imaging diagnostic. Performance was evaluated using a pseudo-MTF derived from a simulated wave pattern test object.

Marks, Daniel G.↗
DOE OSTI2015

Schwinger-variational-principle theory of collisions in the presence of multiple potentials

A theoretical method for treating collisions in the presence of multiple potentials is developed by employing the Schwinger variational principle. The current treatment agrees with the local (regularized) frame transformation theory and extends its capabilities. Specifically, the Schwinger variational approach gives results without the divergences that need to be regularized in other methods. Furthermore, it provides a framework to identify the origin of these singularities and possibly improve the local frame transformation. Here, we have used the method to obtain the scattering parameters for different confining potentials symmetric in x,y. The method is also used to treat photodetachment processes in the presence of various confining potentials, thereby highlighting effects of the infinitely many closed channels. Two general features predicted are the vanishing of the total photoabsorption probability at every channel threshold and the occurrence of resonances below the channel thresholds for negative scattering lengths. In addition, the case of negative-ion photodetachment in the presence of uniform magnetic fields is also considered where unique features emerge at large scattering lengths.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Discovery of 1-5 Hz flaring at high luminosity in SAX J1808.4-3658

We report the discovery of a 1-5 Hz X-ray flaring phenomenon observed at >30 mCrab near peak luminosity in the 2008 and 2011 outbursts of the accreting millisecond X-ray pulsar SAX J1808.4-3658 in observations with the Rossi X-ray Timing Explorer. In each of the two outbursts this high luminosity flaring is seen for ∼3 continuous days and switches on and off on a timescale of 1-2 hr. The flaring can be seen directly in the light curve, where it shows sharp spikes of emission at quasi-regular separation. In the power spectrum it produces a broad noise component, which peaks at 1-5 Hz. The total 0.05-10 Hz variability has a fractional rms amplitude of 20%-45%, well in excess of the 8%-12% rms broadband noise usually seen in power spectra of SAX J1808.4-3658. We perform a detailed timing analysis of the flaring and study its relation to the 401 Hz pulsations. We find that the pulse amplitude varies proportionally with source flux through all phases of the flaring, indicating that the flaring is likely due to mass density variations created at or outside the magnetospheric boundary. We suggest that this 1-5 Hz flaring is a high mass accretion rate version of the 0.5-2 Hz flaring which is known to occur at low luminosity (<13 mCrab), late in the tail of outbursts of SAX J1808.4-3658. We propose the dead-disk instability, previously suggested as the mechanism for the 0.5-2 Hz flaring, as a likely mechanism for the high luminosity flaring reported here.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

SU-D-206-03: Segmentation Assisted Fast Iterative Reconstruction Method for Cone-Beam CT

Purpose: Total Variation (TV) based iterative reconstruction (IR) methods enable accurate CT image reconstruction from low-dose measurements with sparse projection acquisition, due to the sparsifiable feature of most CT images using gradient operator. However, conventional solutions require large amount of iterations to generate a decent reconstructed image. One major reason is that the expected piecewise constant property is not taken into consideration at the optimization starting point. In this work, we propose an iterative reconstruction method for cone-beam CT (CBCT) using image segmentation to guide the optimization path more efficiently on the regularization term at the beginning of the optimization trajectory. Methods: Our method applies general knowledge that one tissue component in the CT image contains relatively uniform distribution of CT number. This general knowledge is incorporated into the proposed reconstruction using image segmentation technique to generate the piecewise constant template on the first-pass low-quality CT image reconstructed using analytical algorithm. The template image is applied as an initial value into the optimization process. Results: The proposed method is evaluated on the Shepp-Logan phantom of low and high noise levels, and a head patient. The number of iterations is reduced by overall 40%. Moreover, our proposed method tends to generate a smoother reconstructed image with the same TV value. Conclusion: We propose a computationally efficient iterative reconstruction method for CBCT imaging. Our method achieves a better optimization trajectory and a faster convergence behavior. It does not rely on prior information and can be readily incorporated into existing iterative reconstruction framework. Our method is thus practical and attractive as a general solution to CBCT iterative reconstruction. This work is supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LR16F010001), National High-tech R&D Program for Young Scientists by the Ministry of Science and Technology of China (Grant No. 2015AA020917).

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

The effect of autoionization on the HBr + X 2 Π 3/2,1/2 state photoelectron angular distributions

A double-imaging photoelectron-photoion spectrometer and synchrotron radiation have been used to measure the HBr + X 2 Π 3/2 v + = 0, 1, 2 and the 2 Π 1/2 v + = 0 state photoelectron angular distributions, as characterized by the anisotropy parameter β , the total ion yield, and the threshold photoelectron spectrum. Particular attention has been focussed on the photon energy range between the 2 Π 3/2 and the 2 Π 1/2 spin–orbit components of the ground ionic state. This region encompasses Rydberg states, belonging to series converging onto the upper 2 Π 1/2 ionization limit, which may decay by autoionization into the 2 Π 3/2 ionization continuum. A detailed study has been performed on the effects of autoionization on the 2 Π 3/2 v + = 0 state photoelectron angular distributions. Furthermore, the observed energy dependent variations in the β -values exhibit a regular pattern that correlates with excitation into members of a very broad d-type Rydberg series. Additional rapid variations in the β -parameters, which occur over a narrow energy range, appear to coincide with sharp autoionizing Rydberg states belonging to s, p and d series. The present experimental results for the HBr + X 2 Π 3/2 v + = 0 state photoelectron anisotropy parameter are compared to previously reported theoretical predictions and to earlier studies of the Kr + 4p 5 2 P 3/2 state β -parameter. The threshold photoelectron spectrum of the X 2 Π 3/2 v + = 0 band exhibits partially resolved rotational structure. A simulation of this structure yields an ionization threshold of 11.6673 ± 0.0010 eV, which is consistent with previous measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions

Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.

97 MATHEMATICS AND COMPUTING↗