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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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DOE OSTI2023

Microscopic calculation of fission product yields for odd-mass nuclei

Fission data are essential inputs to reaction networks involved in nucleosynthesis simulations and nuclear forensics. In such applications as well as in the description of multichance fission, the characteristics of fission for odd-mass nuclei are just as important as those for even-even nuclei. The fission theories that aim at explicitly describing fission dynamics are typically based on some variant of the nuclear mean-field theory. In such cases, the treatment of systems with an odd number of particles is markedly more involved, both formally and computationally. In this article, we use the blocking prescription of the Hartree-Fock-Bogoliubov theory with Skyrme energy functionals to compute the deformation properties of odd-mass uranium isotopes. We show that the resulting fission fragment distributions depend quite significantly on the spin of the odd neutron. By direct calculation of the spin distribution of the fissioning nucleus, we propose a methodology to rigorously predict the charge and mass distributions in odd-mass nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Diffusive dynamics of critical fluctuations near the QCD critical point

A quantitatively reliable theoretical description of the dynamics of fluctuations in nonequilibrium is indispensable in the experimental search for the QCD critical point by means of ultrarelativistic heavy-ion collisions. Herein we consider the fluctuations of the net-baryon density which becomes the slow, critical mode near the critical point. Due to net-baryon number conservation the dynamics is described by the fluid dynamical diffusion equation, which we extend to contain a white noise stochastic current. Including nonlinear couplings from the 3d Ising model universality class in the free energy functional, we solve the fully interacting theory in a finite size system. We observe that purely Gaussian white noise generates non-Gaussian fluctuations, but finite size effects and exact net-baryon number conservation lead to significant deviations from the expected behavior in equilibrated systems. In particular the skewness shows a qualitative deviation from infinite volume expectations.With this benchmark established we study the real-time dynamics of the fluctuations. We recover the expected dynamical scaling behavior and observe retardation effects and the impact of critical slowing down near the pseudocritical temperature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Freely jointed chain models with extensible links

We report analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Fast forward to the classical adiabatic invariant

We show how the classical action, an adiabatic invariant, can be preserved under nonadiabatic conditions. Specifically, for a time-dependent Hamiltonian H = p 2 /2m + U (q,t) in one degree of freedom, and for an arbitrary choice of action I 0 , we construct a so-called fast-forward potential energy function V FF (q,t) that, when added to H, guides all trajectories with initial action I 0 to end with the same value of action. Here, we use this result to construct a local dynamical invariant J (q,p,t) whose value remains constant along these trajectories. We illustrate our results with numerical simulations. Finally, we sketch how our classical results may be used to design approximate quantum shortcuts to adiabaticity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Accurate macromolecular crystallographic refinement: incorporation of the linear scaling, semiempirical quantum-mechanics program DivCon into the PHENIX refinement package

Semiempirical quantum-chemical X-ray macromolecular refinement using the program DivCon integrated with PHENIX is described. Macromolecular crystallographic refinement relies on sometimes dubious stereochemical restraints and rudimentary energy functionals to ensure the correct geometry of the model of the macromolecule and any covalently bound ligand(s). The ligand stereochemical restraint file (CIF) requires a priori understanding of the ligand geometry within the active site, and creation of the CIF is often an error-prone process owing to the great variety of potential ligand chemistry and structure. Stereochemical restraints have been replaced with more robust functionals through the integration of the linear-scaling, semiempirical quantum-mechanics (SE-QM) program DivCon with the PHENIX X-ray refinement engine. The PHENIX/DivCon package has been thoroughly validated on a population of 50 protein–ligand Protein Data Bank (PDB) structures with a range of resolutions and chemistry. The PDB structures used for the validation were originally refined utilizing various refinement packages and were published within the past five years. PHENIX/DivCon does not utilize CIF(s), link restraints and other parameters for refinement and hence it does not make as many a priori assumptions about the model. Across the entire population, the method results in reasonable ligand geometries and low ligand strains, even when the original refinement exhibited difficulties, indicating that PHENIX/DivCon is applicable to both single-structure and high-throughput crystallography.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Modified Virtual Oscillator Based Operation of Grid Forming Converters with Single Voltage Sensor

Virtual oscillator based control architecture for grid forming converter with inner current control loop for additional objective accomplishments is proposed in this paper. In general, virtual oscillator is based on Lienard type of oscillator equation with a cubic nonlinearity. Virtual oscillator alone cannot accommodate unbalanced or harmonic mitigation while operating converters in grid forming mode. Therefore, to accomplish better tracking performance, incorporating the provision for nonlinear and/or unbalanced loads, an inner current control loop is utilized which is based upon Lyapunov energy function type control architecture due to its advantages. To reduce the overall cost of implementation and ensure proper phase difference in the generated voltages, the implemented virtual oscillator operates with only one voltage feedback from the point of common coupling as presented in this paper. To verify the effectiveness of the proposed approach, the overall system has been modeled in MATTLAB/Simulink and PLECS domain and case studies showing the successful production of low harmonic load voltages under nonideal loading condition along with other important results are presented in this paper.

dual second order generalized integrator↗
DOE OSTI2025

Advancing the Frontiers of Deep Learning for Low-Dose 3D Cone-Beam CT Reconstruction

X-ray computed tomography (CT) is an important noninvasive medical imaging modality for studying the structural details of internal organs. Image reconstruction in CT is an inverse problem of recovering an object's internal structure from the absorption profile of X-ray beams (sinogram) measured using a detector. The classical variational approach for CT reconstruction minimizes an energy functional using an appropriate iterative algorithm. Motivated by the success of deep learning (DL), researchers have begun to leverage training data and enhanced computing capabilities in recent years to produce high-fidelity reconstructed images. Nonetheless, much of the academic research in DL algorithms for CT has focused primarily on the two-dimensional setting (with simplified forward operators and noise model) for proofs-of-concept, and a comprehensive benchmarking of various classical and data-driven CT reconstruction approaches has not beenundertaken. The key objective of our CT reconstruction grand challenge was to promote methodological advancements for both classical and DL-based approaches for clinical CT with a reasonably accurately simulated 3D CT forward operator and noise model. We have utilized the publicly available LIDC-IDRI dataset and simulated sinograms and FDK images corresponding to two dose levels (clinical- and low-dose, constituting two tracks of the challenge) starting from the normal-dose images as the ground truth. In this paper, we summarize the motivation, context, and results of our challenge, and highlight the future research directions in DL for clinical CT.

X-ray tomography↗
DOE OSTI2014

A region-appearance-based adaptive variational model for 3D liver segmentation

Purpose: Liver segmentation from computed tomography images is a challenging task owing to pixel intensity overlapping, ambiguous edges, and complex backgrounds. The authors address this problem with a novel active surface scheme, which minimizes an energy functional combining both edge- and region-based information. Methods: In this semiautomatic method, the evolving surface is principally attracted to strong edges but is facilitated by the region-based information where edge information is missing. As avoiding oversegmentation is the primary challenge, the authors take into account multiple features and appearance context information. Discriminative cues, such as multilayer consecutiveness and local organ deformation are also implicitly incorporated. Case-specific intensity and appearance constraints are included to cope with the typically large appearance variations over multiple images. Spatially adaptive balancing weights are employed to handle the nonuniformity of image features. Results: Comparisons and validations on difficult cases showed that the authors’ model can effectively discriminate the liver from adhering background tissues. Boundaries weak in gradient or with no local evidence (e.g., small edge gaps or parts with similar intensity to the background) were delineated without additional user constraint. With an average surface distance of 0.9 mm and an average volume overlap of 93.9% on the MICCAI data set, the authors’ model outperformed most state-of-the-art methods. Validations on eight volumes with different initial conditions had segmentation score variances mostly less than unity. Conclusions: The proposed model can efficiently delineate ambiguous liver edges from complex tissue backgrounds with reproducibility. Quantitative validations and comparative results demonstrate the accuracy and efficacy of the model.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

Physics-based shape matching for intraoperative image guidance

Purpose: Soft-tissue deformations can severely degrade the validity of preoperative planning data during computer assisted interventions. Intraoperative imaging such as stereo endoscopic, time-of-flight or, laser range scanner data can be used to compensate these movements. In this context, the intraoperative surface has to be matched to the preoperative model. The shape matching is especially challenging in the intraoperative setting due to noisy sensor data, only partially visible surfaces, ambiguous shape descriptors, and real-time requirements. Methods: A novel physics-based shape matching (PBSM) approach to register intraoperatively acquired surface meshes to preoperative planning data is proposed. The key idea of the method is to describe the nonrigid registration process as an electrostatic–elastic problem, where an elastic body (preoperative model) that is electrically charged slides into an oppositely charged rigid shape (intraoperative surface). It is shown that the corresponding energy functional can be efficiently solved using the finite element (FE) method. It is also demonstrated how PBSM can be combined with rigid registration schemes for robust nonrigid registration of arbitrarily aligned surfaces. Furthermore, it is shown how the approach can be combined with landmark based methods and outline its application to image guidance in laparoscopic interventions. Results: A profound analysis of the PBSM scheme based on in silico and phantom data is presented. Simulation studies on several liver models show that the approach is robust to the initial rigid registration and to parameter variations. The studies also reveal that the method achieves submillimeter registration accuracy (mean error between 0.32 and 0.46 mm). An unoptimized, single core implementation of the approach achieves near real-time performance (2 TPS, 7–19 s total registration time). It outperforms established methods in terms of speed and accuracy. Furthermore, it is shown that the method is able to accurately match partial surfaces. Finally, a phantom experiment demonstrates how the method can be combined with stereo endoscopic imaging to provide nonrigid registration during laparoscopic interventions. Conclusions: The PBSM approach for surface matching is fast, robust, and accurate. As the technique is based on a preoperative volumetric FE model, it naturally recovers the position of volumetric structures (e.g., tumors and vessels). It cannot only be used to recover soft-tissue deformations from intraoperative surface models but can also be combined with landmark data from volumetric imaging. In addition to applications in laparoscopic surgery, the method might prove useful in other areas that require soft-tissue registration from sparse intraoperative sensor data (e.g., radiation therapy)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

SU-E-J-131: Augmenting Atlas-Based Segmentation by Incorporating Image Features Proximal to the Atlas Contours

Purpose: For facilitating the current automatic segmentation, in this work we propose a narrow-shell strategy to enhance the information of each contour in the library and to improve the accuracy of the exiting atlas-based approach. Methods: In setting up an atlas-based library, we include not only the coordinates of contour points, but also the image features adjacent to the contour. 139 planning CT scans with normal appearing livers obtained during their radiotherapy treatment planning were used to construct the library. The CT images within the library were registered each other using affine registration. A nonlinear narrow shell with the regional thickness determined by the distance between two vertices alongside the contour. The narrow shell was automatically constructed both inside and outside of the liver contours. The common image features within narrow shell between a new case and a library case were first selected by a Speed-up Robust Features (SURF) strategy. A deformable registration was then performed using a thin plate splines (TPS) technique. The contour associated with the library case was propagated automatically onto the images of the new patient by exploiting the deformation field vectors. The liver contour was finally obtained by employing level set based energy function within the narrow shell. The performance of the proposed method was evaluated by comparing quantitatively the auto-segmentation results with that delineated by a physician. Results: Application of the technique to 30 liver cases suggested that the technique was capable of reliably segment organs such as the liver with little human intervention. Compared with the manual segmentation results by a physician, the average and discrepancies of the volumetric overlap percentage (VOP) was found to be 92.43%+2.14%. Conclusion: Incorporation of image features into the library contours improves the currently available atlas-based auto-contouring techniques and provides a clinically practical solution for auto-segmentation. This work is supported by NIH/NIBIB (1R01-EB016777), National Natural Science Foundation of China (No.61471226 and No.61201441), Research funding from Shandong Province (No.BS2012DX038 and No.J12LN23), and Research funding from Jinan City (No.201401221 and No.20120109)

60 APPLIED LIFE SCIENCES↗
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 OSTI2015

3D liver segmentation using multiple region appearances and graph cuts

Purpose: Efficient and accurate 3D liver segmentations from contrast-enhanced computed tomography (CT) images play an important role in therapeutic strategies for hepatic diseases. However, inhomogeneous appearances, ambiguous boundaries, and large variance in shape often make it a challenging task. The existence of liver abnormalities poses further difficulty. Despite the significant intensity difference, liver tumors should be segmented as part of the liver. This study aims to address these challenges, especially when the target livers contain subregions with distinct appearances. Methods: The authors propose a novel multiregion-appearance based approach with graph cuts to delineate the liver surface. For livers with multiple subregions, a geodesic distance based appearance selection scheme is introduced to utilize proper appearance constraint for each subregion. A special case of the proposed method, which uses only one appearance constraint to segment the liver, is also presented. The segmentation process is modeled with energy functions incorporating both boundary and region information. Rather than a simple fixed combination, an adaptive balancing weight is introduced and learned from training sets. The proposed method only calls initialization inside the liver surface. No additional constraints from user interaction are utilized. Results: The proposed method was validated on 50 3D CT images from three datasets, i.e., Medical Image Computing and Computer Assisted Intervention (MICCAI) training and testing set, and local dataset. On MICCAI testing set, the proposed method achieved a total score of 83.4 ± 3.1, outperforming nonexpert manual segmentation (average score of 75.0). When applying their method to MICCAI training set and local dataset, it yielded a mean Dice similarity coefficient (DSC) of 97.7% ± 0.5% and 97.5% ± 0.4%, respectively. These results demonstrated the accuracy of the method when applied to different computed tomography (CT) datasets. In addition, user operator variability experiments showed its good reproducibility. Conclusions: A multiregion-appearance based method is proposed and evaluated to segment liver. This approach does not require prior model construction and so eliminates the burdens associated with model construction and matching. The proposed method provides comparable results with state-of-the-art methods. Validation results suggest that it may be suitable for the clinical use.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Interactive contour delineation of organs at risk in radiotherapy: Clinical evaluation on NSCLC patients

Purpose: Accurate delineation of organs at risk (OARs) on computed tomography (CT) image is required for radiation treatment planning (RTP). Manual delineation of OARs being time consuming and prone to high interobserver variability, many (semi-) automatic methods have been proposed. However, most of them are specific to a particular OAR. Here, an interactive computer-assisted system able to segment various OARs required for thoracic radiation therapy is introduced. Methods: Segmentation information (foreground and background seeds) is interactively added by the user in any of the three main orthogonal views of the CT volume and is subsequently propagated within the whole volume. The proposed method is based on the combination of watershed transformation and graph-cuts algorithm, which is used as a powerful optimization technique to minimize the energy function. The OARs considered for thoracic radiation therapy are the lungs, spinal cord, trachea, proximal bronchus tree, heart, and esophagus. The method was evaluated on multivendor CT datasets of 30 patients. Two radiation oncologists participated in the study and manual delineations from the original RTP were used as ground truth for evaluation. Results: Delineation of the OARs obtained with the minimally interactive approach was approved to be usable for RTP in nearly 90% of the cases, excluding the esophagus, which segmentation was mostly rejected, thus leading to a gain of time ranging from 50% to 80% in RTP. Considering exclusively accepted cases, overall OARs, a Dice similarity coefficient higher than 0.7 and a Hausdorff distance below 10 mm with respect to the ground truth were achieved. In addition, the interobserver analysis did not highlight any statistically significant difference, at the exception of the segmentation of the heart, in terms of Hausdorff distance and volume difference. Conclusions: An interactive, accurate, fast, and easy-to-use computer-assisted system able to segment various OARs required for thoracic radiation therapy has been presented and clinically evaluated. The introduction of the proposed system in clinical routine may offer valuable new option to radiation oncologists in performing RTP.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

TU-H-CAMPUS-IeP3-01: Simultaneous PET Restoration and PET/CT Co-Segmentation Using a Variational Method

Purpose: PET images are usually blurred due to the finite spatial resolution, while CT images suffer from low contrast. Segment a tumor from either a single PET or CT image is thus challenging. To make full use of the complementary information between PET and CT, we propose a novel variational method for simultaneous PET image restoration and PET/CT images co-segmentation. Methods: The proposed model was constructed based on the Γ-convergence approximation of Mumford-Shah (MS) segmentation model for PET/CT co-segmentation. Moreover, a PET de-blur process was integrated into the MS model to improve the segmentation accuracy. An interaction edge constraint term over the two modalities were specially designed to share the complementary information. The energy functional was iteratively optimized using an alternate minimization (AM) algorithm. The performance of the proposed method was validated on ten lung cancer cases and five esophageal cancer cases. The ground truth were manually delineated by an experienced radiation oncologist using the complementary visual features of PET and CT. The segmentation accuracy was evaluated by Dice similarity index (DSI) and volume error (VE). Results: The proposed method achieved an expected restoration result for PET image and satisfactory segmentation results for both PET and CT images. For lung cancer dataset, the average DSI (0.72) increased by 0.17 and 0.40 than single PET and CT segmentation. For esophageal cancer dataset, the average DSI (0.85) increased by 0.07 and 0.43 than single PET and CT segmentation. Conclusion: The proposed method took full advantage of the complementary information from PET and CT images. This work was supported in part by the National Cancer Institute Grants R01CA172638. Shan Tan and Laquan Li were supported in part by the National Natural Science Foundation of China, under Grant Nos. 60971112 and 61375018.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with these quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

A Nonlocal Feature-Driven Exemplar-Based Approach for Image Inpainting

Here, we present a nonlocal variational image completion technique which admits simultaneous inpainting of multiple structures and textures in a unified framework. The recovery of geometric structures is achieved by using general convolution operators as a measure of behavior within an image. These are combined with a nonlocal exemplar-based approach to exploit the self-similarity of an image in the selected feature domains and to ensure the inpainting of textures. We also introduce an anisotropic patch distance metric to allow for better control of the feature selection within an image and present a nonlocal energy functional based on this metric. Finally, we derive an optimization algorithm for the proposed variational model and examine its validity experimentally with various test images.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Algebraic Multigrid with Filtering: An Efficient Preconditioner for Interior Point Methods in Large-Scale Contact Mechanics Optimization

Large-scale contact mechanics simulations are crucial in many engineering fields such as structural design and manufacturing. In the frictionless case, contact can be modeled by minimizing an energy functional; however, these problems are often nonlinear, nonconvex, and increasingly difficult to solve as mesh resolution increases. In this work, we employ a Newton-based interior-point (IP) filter line-search method, an effective approach for large-scale constrained optimization. While this method converges rapidly, each iteration requires solving a large saddle-point linear system that becomes ill-conditioned as the optimization process converges, largely due to IP treatment of the contact constraints. Such ill-conditioning can hinder solver scalability and increase iteration counts with mesh refinement. Here, to address this, we introduce a novel preconditioner, algebraic multigrid with filtering (AMGF), tailored to the Schur complement of the saddle-point system. Building on the classical AMG solver, commonly used for elasticity, we augment it with a specialized subspace correction that filters near null space components introduced by contact interface constraints. Through theoretical analysis and numerical experiments on a range of linear and nonlinear contact problems, we demonstrate that the proposed solver achieves mesh independent convergence and maintains robustness against the ill-conditioning that notoriously plagues IP methods. These results indicate that AMGF makes contact mechanics simulations more tractable and broadens the applicability of Newton-based IP methods in challenging engineering scenarios. More broadly, AMGF is well suited for problems, optimization or otherwise, where solver performance is limited by a low-dimensional subspace, such as those arising from localized constraints, interface conditions, or model heterogeneities. This makes the method widely applicable beyond contact mechanics and constrained optimization.

Mathematics and Computing↗
DOE OSTI2021

On a nonlocal Cahn–Hilliard model permitting sharp interfaces

A nonlocal Cahn–Hilliard model with a non-smooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactions between particles, a nonlocal Ginzburg–Landau energy functional is defined which recovers the classical (local) model as the extent of nonlocal interactions vanish. In contrast to the local Cahn–Hilliard problem that always leads to diffuse interfaces, the proposed nonlocal model can lead to a strict separation into pure phases of the substance. In this work, the lack of smoothness of the potential is essential to guarantee the aforementioned sharp-interface property. Mathematically, this introduces additional inequality constraints that, in a weak formulation, lead to a coupled system of variational inequalities which at each time instance can be restated as a constrained optimization problem. We prove the well-posedness and regularity of the semi-discrete and continuous in time weak solutions, and derive the conditions under which pure phases are admitted. Moreover, we develop discretizations of the problem based on finite element methods and implicit–explicit time-stepping methods that can be realized efficiently. Finally, we illustrate our theoretical findings through several numerical experiments in one and two spatial dimensions that highlight the differences in features of local and nonlocal solutions and also the sharp interface properties of the nonlocal model.

97 MATHEMATICS AND COMPUTING↗