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Critical pore radius and transport properties of disordered hard- and overlapping-sphere models

Physical Review E 2021年第1期104卷 014127-014127页

作者： Michael A. Klatt Robert M. Ziff Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Institut für Theoretische Physik FAU Erlangen-Nürnberg Staudtstr. 7 91058 Erlangen Germany Center for the Study of Complex Systems and Department of Chemical Engineering University of Michigan Ann Arbor Michigan 48109 USA Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δc. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δc is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ2〉, which is easier to determine than δc. Here, we compare δc to the second moment of the pore size 〈δ2〉, and indeed confirm that, for all porosities and all models considered, δc2 is to a good approximation proportional to 〈δ2〉. However, unlike 〈δ2〉, the permeability estimate based on δc2 does not predict the correct ranking of k for our models. Thus, we confirm 〈δ2〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targete

关键词： Geophysical networks Materials Patterns in complex systems

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Characterization of void space, large-scale structure, and transport properties of maximally random jammed packings of superballs

arXiv

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arXiv 2021年

作者： Maher, Charles Emmett Stillinger, Frank H. Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by |x1|2p + |x2|2p + |x3|2p ≤ 1, where p ∈ (0, ∞) is a deformation parameter indicating to what extent the shape deviates from a sphere. As p increases from the sphere point (p = 1), the superball tends to a cuboidal shape and approaches a cube in the p → ∞ limit. As p → 0.5, it approaches an octahedron, becomes a concave body with octahedral symmetry for p ¯) vary nonanalytically as p diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings with 0.85 ≤ p ≤ 1.50. To supplement the previous work on such packings, we characterize their large-scale structure by examining the behaviors of their structure factors S(Q) and spectral densities χV (Q), as the wave number Q tends to zero, and find that these packings are effectively hyperuniform for all values of p examined. We show that the mean width w¯ is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. Moreover, we compute the complementary cumulative pore-size distribution F (δ) and find that the pore sizes tend to decrease as |1 − p| increases. From F (δ), we estimate how the fluid permeability, mean survival time, and principal diffusion relaxation time vary as a function of p. Additionally, we compute the diffusion "spreadability" S(t) [Torquato, Phys. Rev. E, 104, 054102, (2021)] of these packings and find that the long-time power-law scaling indicates these packings are hyperuniform with a small-Q power law scaling of the spectral density χV (Q) ∼ Qα with an exponent α that ranges from 0.64 at th

关键词： Spheres

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Simulating Cardiac Fluid Dynamics in the Human Heart

arXiv

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arXiv 2023年

作者： Davey, Marshall Puelz, Charles Rossi, Simone Smith, Margaret Anne Wells, David R. Sturgeon, Gregory M. Segars, W. Paul Vavalle, John P. Peskin, Charles S. Griffith, Boyce E. University of North Carolina Chapel HillNC United States Department of Pediatrics-Cardiology Baylor College of Medicine Texas Children’s Hospital HoustonTX United States Department of Mathematics University North Carolina Chapel HillNC United States Department of Radiology Duke University Medical Center DurhamNC United States Division of Cardiology Department of Medicine University of North Carolina School of Medicine Chapel HillNC United States Courant Institute of Mathematical Sciences New York University New YorkNY United States Departments of Mathematics and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

Cardiac fluid dynamics fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin, flexible valve leaflets. There has been longstanding scientific, engineering, and medical interest in creating mathematical models of the heart that capture, explain, and predict these fluid-structure interactions. However, existing computational models that account for interactions among the blood, the actively contracting myocardium, and the cardiac valves are limited in their abilities to predict valve performance, resolve fine-scale flow features, or use realistic descriptions of tissue biomechanics. Here we introduce and benchmark a comprehensive mathematical model of cardiac fluid dynamics in the human heart. A unique feature of our model is that it incorporates biomechanically detailed descriptions of all major cardiac structures that are calibrated using tensile tests of human tissue specimens to reflect the heart’s microstructure. Further, it is the first fluid-structure interaction model of the heart that provides anatomically and physiologically detailed representations of all four cardiac valves. We demonstrate that this integrative model generates physiologic dynamics, including realistic pressure-volume loops that automatically capture isovolumetric contraction and relaxation, and predicts fine-scale flow features. None of these outputs are prescribed;instead, they emerge from interactions within our comprehensive description of cardiac physiology. Such models can serve as tools for predicting the impacts of medical devices or clinical interventions. They also can serve as platforms for mechanistic studies of cardiac pathophysiology and dysfunction, including congenital defects, cardiomyopathies, and heart failure, that are difficult or impossible to perform in patients. Copyright © 2023, The Authors. All rights reserved.

关键词： Heart

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Flexibility and rigidity in steady fluid motion

arXiv

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arXiv 2020年

作者： Constantin, Peter Drivas, Theodore D. Ginsberg, Daniel Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Stony Brook University Stony BrookNY11794 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable steady solutions with no stagnation points occupying a two-dimensional periodic channel, or axisymmetric solutions in (hollowed out) cylinder, must have certain structural symmetries. It is additionally shown that such solutions can be deformed to occupy domains which are themselves small perturbations of the base domain. As application of the general scheme, Arnol'd stable solutions are shown to be structurally stable. Copyright © 2020, The Authors. All rights reserved.

关键词： Rigidity

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A Model of Fluid-Structure and Biochemical Interactions for Applications to Subclinical Leaflet Thrombosis

arXiv

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arXiv 2022年

作者： Barrett, Aaron Brown, Jordan A. Smith, Margaret Anne Woodward, Andrew Vavalle, John P. Kheradvar, Arash Griffith, Boyce E. Fogelson, Aaron L. Department of Mathematics University of Utah Salt Lake CityUT United States Department of Mathematics University of North Carolina Chapel HillNC United States Advanced Medical Imaging Lab University of North Carolina Medical Center Chapel HillNC United States University of North Carolina School of Medicine Chapel HillNC United States Division of Cardiology Department of Medicine University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of California Irvine IrvineCA United States Department of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States Department of Mathematics and Biomedical Engineering University of Utah Salt Lake CityUT United States

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis in which they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction. © 2022, CC BY-SA.

关键词： Deposition

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Isotope effects in molecular structures and electronic properties of liquid water via deep potential molecular dynamics based on the SCAN functional

引用

Physical Review B 2020年第21期102卷 214113-214113页

作者： Jianhang Xu Chunyi Zhang Linfeng Zhang Mohan Chen Biswajit Santra Xifan Wu Department of Physics Temple University Philadelphia Pennsylvania 19122 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA CAPT HEDPS College of Engineering Peking University Beijing 100871 China Institute for Computational Molecular Science Temple University Philadelphia Pennsylvania 19122 USA

Feynman path-integral deep potential molecular dynamics (PI-DPMD) calculations have been employed to study both light (H2O) and heavy water (D2O) within the isothermalisobaric ensemble. In particular, the deep neural network is trained based on ab initio data obtained from the strongly constrained and appropriately normed (SCAN) exchange-correlation functional. Because of the lighter mass of hydrogen than deuteron, the properties of light water are more influenced by nuclear quantum effect than those of heavy water. Clear isotope effects are observed and analyzed in terms of hydrogen-bond structure and electronic properties of water that are closely associated with experimental observables. The molecular structures of both liquid H2O and D2O agree well with the data extracted from scattering experiments. The delicate isotope effects on radial distribution functions and angular distribution functions are well reproduced as well. Our approach demonstrates that deep neural network combined with SCAN functional based ab initio molecular dynamics provides an accurate theoretical tool for modeling water and its isotope effects.

关键词： Atomic & molecular structure Electronic structure Isotope effect Water Ab initio calculations Density functional theory Machine learning Molecular dynamics Path-integral methods

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Local two-sample testing over graphs and point-clouds by random-walk distributions

arXiv

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arXiv 2020年

作者： Landa, Boris Qu, Rihao Chang, Joseph Kluger, Yuval Program in Applied Mathematics Yale University Department of Pathology Yale University School of Medicine Department of Statistics and Data Science Yale University Interdepartmental Program in Computational Biology and Bioinformatics Yale University Department of Immunology Yale School of Medicine

Rejecting the null hypothesis in two-sample testing is a fundamental tool for scientific discovery. Yet, aside from concluding that two samples do not come from the same probability distribution, it is often of interest to characterize how the two distributions differ. Given samples from two densities f1and f0, we consider the task of localizing occurrences of the inequality f1> f0. To avoid the challenges associated with high-dimensional space, we propose a general hypothesis testing framework where hypotheses are formulated adaptively to the data by conditioning on the combined sample from the two densities. We then investigate a special case of this framework where the notion of locality is captured by a random walk on a weighted graph constructed over this combined sample. We derive a tractable testing procedure for this case employing a type of scan statistic, and provide non-asymptotic lower bounds on the power and accuracy of our test to detect whether f1> f0in a local sense. Furthermore, we characterize the test's consistency according to a certain problem-hardness parameter, and show that our test achieves the minimax detection rate for this parameter. We conduct numerical experiments to validate our method, and demonstrate our approach on two real-world applications: detecting and localizing arsenic well contamination across the United States, and analyzing two-sample single-cell RNA sequencing data from melanoma *** Codes 62G10 Copyright © 2020, The Authors. All rights reserved.

关键词： Random processes

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Modeling subgrid-scale forces by spatial artificial neural networks in large eddy simulation of turbulence

引用

Physical Review Fluids 2020年第5期5卷 054606-054606页

作者： Chenyue Xie Jianchun Wang Weinan E Shenzhen Key Laboratory of Complex Aerospace Flows Center for Complex Flows and Soft Matter Research Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen 518055 People's Republic of China Department of Mathematics Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Spatial artificial neural network (ANN) models are developed for subgrid-scale (SGS) forces in the large eddy simulation (LES) of turbulence. The input features are based on the first-order derivatives of the filtered velocity field at different spatial locations. The correlation coefficients of SGS forces predicted by the spatial artifical neural network (SANN) models with reasonable spatial stencil geometry can be made larger than 0.99 in an a priori analysis, and the relative error of SGS forces can be made smaller than 15%, much smaller than that of the traditional gradient model. In a posteriori analysis, a detailed comparison is made on the results of LES using the SANN model, implicit large eddy simulation (ILES), the dynamic Smagorinsky model (DSM), and the dynamic mixed model (DMM) at grid resolution of 643. It is shown that the SANN model performs better than the ILES, DSM, and DMM models in the prediction of the spectrum and other statistical properties of the velocity field, as well as the instantaneous flow structures. These results suggest that artificial neural network with consideration of spatial characteristics is a very effective tool for developing advanced SGS models in LES of turbulence.

关键词： Compressible flows Turbulence Artificial neural networks

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Modeling liquid water by climbing up Jacob’s ladder in density functional theory facilitated by using deep neural network potentials

arXiv

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arXiv 2021年

作者： Zhang, Chunyi Tang, Fujie Chen, Mohan Zhang, Linfeng Qiu, Diana Y. Perdew, John P. Klein, Michael L. Wu, Xifan Department of Physics Temple University PhiladelphiaPA19122 United States HEDPS Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mechanical Engineering and Materials Science Yale University New HavenCT06520 United States Department of Chemistry Temple University PhiladelphiaPA19122 United States Institute for Computational Molecular Science Temple University PhiladelphiaPA19122 United States

Within the framework of Kohn-Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric-isothermal ensemble. In order to generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water towards the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. © 2021, CC BY.

关键词： Deep neural networks

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Overview of the Head and Neck Tumor Segmentation for Magnetic Resonance Guided Applications (HNTS-MRG) 2024 Challenge

arXiv

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arXiv 2024年

作者： Wahid, Kareem A. Dede, Cem El-Habashy, Dina M. Kamel, Serageldin Rooney, Michael K. Khamis, Yomna Abdelaal, Moamen R.A. Ahmed, Sara Corrigan, Kelsey L. Chang, Enoch Dudzinski, Stephanie O. Salzillo, Travis C. McDonald, Brigid A. Mulder, Samuel L. McCullum, Lucas Alakayleh, Qusai Sjogreen, Carlos He, Renjie Mohamed, Abdallah S.R. Lai, Stephen Y. Christodouleas, John P. Schaefer, Andrew J. Naser, Mohamed A. Fuller, Clifton D. Department of Radiation Oncology The University of Texas MD Anderson Cancer HoustonTX United States Department of Imaging Physics The University of Texas MD Anderson Cancer HoustonTX United States Transitional Year Program Corewell Health Wiliam Beaumont Royal OakMI United States Department of Radiation Oncology University of Maryland School of Medicine BaltimoreMD United States Department of Clinical Oncology and Nuclear Medicine Faculty of Medicine Alexandria University Alexandria Egypt UT MD Anderson Cancer Center UTHealth Houston Graduate School of Biomedical Sciences Houston United States Department of Radiation Oncology Baylor College of Medicine HoustonTX United States Department of Head and Neck Surgery The University of Texas MD Anderson Cancer HoustonTX United States Elekta AtlantaGA United States Department of Computational Applied Mathematics and Operations Research Rice University HoustonTX United States

Magnetic resonance (MR)-guided radiation therapy (RT) is enhancing head and neck cancer (HNC) treatment through superior soft tissue contrast and longitudinal imaging capabilities. However, manual tumor segmentation remains a significant challenge, spurring interest in artificial intelligence (AI)-driven automation. To accelerate innovation in this field, we present the Head and Neck Tumor Segmentation for MR-Guided Applications (HNTS-MRG) 2024 Challenge, a satellite event of the 27th International Conference on Medical Image Computing and Computer Assisted Intervention. This challenge addresses the scarcity of large, publicly available AI-ready adaptive RT datasets in HNC and explores the potential of incorporating multi-timepoint data to enhance RT auto-segmentation performance. Participants tackled two HNC segmentation tasks: automatic delineation of primary gross tumor volume (GTVp) and gross metastatic regional lymph nodes (GTVn) on pre-RT (Task 1) and mid-RT (Task 2) T2-weighted scans. The challenge provided 150 HNC cases for training and 50 for testing, hosted on *** using a Docker submission framework. In total, 19 independent teams from across the world qualified by submitting both their algorithms and corresponding papers, resulting in 18 submissions for Task 1 and 15 submissions for Task 2. Evaluation using the mean aggregated Dice Similarity Coefficient showed top-performing AI methods achieved scores of 0.825 in Task 1 and 0.733 in Task 2. These results surpassed clinician interobserver variability benchmarks, marking significant strides in automated tumor segmentation for MR-guided RT applications in HNC. © 2024, CC BY.

关键词： Magnetic resonance imaging

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