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arXiv 2020年

作者： Zhan, Xiu-Xiu Li, Ziyu Masuda, Naoki Holme, Petter Wang, Huijuan Faculty of Electrical Engineering Mathematics and Computer Science Delft University of Technology Mekelweg 4 Delft2628 CD Netherlands Department of Mathematics University at Buffalo State University of New York Buffalo New YorkNY14260-2900 United States Computational and Data-Enabled Science and Engineering Program University at Buffalo State University of New York Buffalo New YorkNY14260-2900 United States Institute of Innovative Research Tokyo Institute of Technology Yokohama226-8503 Japan

Link prediction can be used to extract missing information, identify spurious interactions as well as forecast network evolution. Network embedding is a methodology to assign coordinates to nodes in a low-dimensional vector space. By embedding nodes into vectors, the link prediction problem can be converted into a similarity comparison task. Nodes with similar embedding vectors are more likely to be connected. Classic network embedding algorithms are random-walk-based. They sample trajectory paths via random walks and generate node pairs from the trajectory paths. The node pair set is further used as the input for a Skip-Gram model, a representative language model that embeds nodes (which are regarded as words) into vectors. In the present study, we propose to replace random walk processes by a spreading process, namely the susceptible-infected (SI) model, to sample paths. Specifically, we propose two SI-spreading-based algorithms, SINE and TSINE, to embed static and temporal networks, respectively. The performance of our algorithms is evaluated by the missing link prediction task in comparison with state-of-the-art static and temporal network embedding algorithms. Results show that SINE and TSINE outperform the baselines across all six empirical datasets. We further find that the performance of SINE is mostly better than TSINE, suggesting that temporal information does not necessarily improve the embedding for missing link prediction. Moreover, we study the effect of the sampling size, quantified as the total length of the trajectory paths, on the performance of the embedding algorithms. The better performance of SINE and TSINE requires a smaller sampling size in comparison with the baseline algorithms. Hence, SI-spreading-based embedding tends to be more applicable to large-scale networks. Copyright © 2020, The Authors. All rights reserved.

关键词： Network embeddings

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Collective behavior of active topological solitons, knotted streamlines, and transport of cargo in liquid crystals

arXiv

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arXiv 2017年

作者： Sohn, Hayley R.O. Ackerman, Paul J. Boyle, Timothy J. Sheetah, Ghadah H. Fornberg, Bengt Smalyukh, Ivan I. Soft Materials Research Center and Materials Science and Engineering Program University of Colorado BoulderCO80309 United States Department of Physics Department of Electrical Computer and Energy Engineering University of Colorado BoulderCO80309 United States Department of Applied Mathematics University of Colorado BoulderCO80309 United States Renewable and Sustainable Energy Institute National Renewable Energy Laboratory University of Colorado BoulderCO80309 United States

Active colloids and liquid crystals are capable of locally converting the macroscopically-supplied energy into directional motion and promise a host of new applications, ranging from drug delivery to cargo transport at the mesoscale. Here we uncover how topological solitons in liquid crystals can locally transform electric energy to translational motion and allow for the transport of cargo along directions dependent on frequency of the applied electric field. By combining polarized optical video microscopy and numerical modeling that reproduces both the equilibrium structures of solitons and their temporal evolution in applied fields, we uncover the physical underpinnings behind this reconfigurable motion and study how it depends on the structure and topology of solitons. We show that, unexpectedly, the directional motion of solitons with and without the cargo arises mainly from the asymmetry in rotational dynamics of molecular ordering in liquid crystal rather than from the asymmetry of fluid flows, as in conventional active soft matter systems. Copyright © 2017, The Authors. All rights reserved.

关键词： Solitons

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Thermal Conductivity of Water at Extreme Conditions

arXiv

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arXiv 2023年

作者： Zhang, Cunzhi Puligheddu, Marcello Zhang, Linfeng Car, Roberto Galli, Giulia Pritzker School of Molecular Engineering University of Chicago ChicagoIL60637 United States Materials Science Division Center for Molecular Engineering Argonne National Laboratory LemontIL60439 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Chemistry University of Chicago ChicagoIL60637 United States

Measuring the thermal conductivity (κ) of water at extreme conditions is a challenging task and few experimental data are available. We predict κ for temperatures and pressures relevant to the conditions of the Earth mantle, between 1,000 and 2,000 K and up to 22 GPa. We employ close to equilibrium molecular dynamics simulations and a deep neural network potential fitted to density functional theory data. We then interpret our results by computing the equation of state of water on a fine grid of points and using a simple model for κ. We find that the thermal conductivity is weakly dependent on temperature and monotonically increases with pressure with an approximate square-root behavior. In addition we show how the increase of κ at high pressure, relative to ambient conditions, is related to the corresponding increase in the sound velocity. Although the relationships between the thermal conductivity, pressure and sound velocity established here are not rigorous, they are sufficiently accurate to allow for a robust estimate of the thermal conductivity of water in a broad range of temperatures and pressures, where experiments are still difficult to perform. Copyright © 2023, The Authors. All rights reserved.

关键词： Thermal conductivity

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Local Divergence-Free Immersed Finite Element-Difference Method Using Composite B-Splines

arXiv

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arXiv 2024年

作者： Li, Lianxia Gruninger, Cole Lee, Jae H. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of 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

In the class of immersed boundary (IB) methods, the choice of the regularized delta function plays a crucial role in transferring information between fluid and solid domains through interpolation and spreading operators. Most prior work using the IB method has used isotropic kernels that do not preserve the divergence-free condition of the velocity field, leading to loss of incompressibility of the solid when interpolating the Eulerian velocity to Lagrangian markers. To address this issue, in simulations involving large deformations of incompressible hyperelastic structures immersed in fluid, researchers often use a volumetric stabilization approach such as adding a volumetric energy term and using modified invariants in the constitutive model of the immersed structure. Composite B-spline (CBS) kernels offer an alternative approach by inherently maintaining the discrete divergence-free property. This work evaluates the performance of CBS kernels in terms of their volume conservation and accuracy, comparing them with several traditional isotropic kernel functions using a construction introduced by Peskin (referred to as IB kernels) and B-spline (BS) kernels. Benchmark tests include pressure-loaded and shear-dominated flows, such as an elastic band under differential pressure loads, a pressurized membrane, a compressed block, Cook’s membrane, a slanted channel flow, and a modified Turek-Hron problem. Additionally, we validate our methodology using a complex fluid-structure interaction model of bioprosthetic heart valve dynamics in a pulse duplicator. Results demonstrate that CBS kernels achieve superior volume conservation compared to conventional isotropic kernels, eliminating the need for additional volumetric stabilization techniques typically required to address instabilities arising from volume conservation errors. Further, CBS kernels achieve convergence on coarser fluid grids, while IB and BS kernels need finer grids for comparable accuracy. Unlike IB and BS ke

关键词： Delta functions

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Configurational entropy of magnetic skyrmions as an ideal gas

arXiv

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arXiv 2019年

作者： Zivieri, R. Tomasello, R. Chubykalo-Fesenko, O. Tiberkevich, V. Carpentieri, M. Finocchio, G. Department of Mathematical and Computer Sciences Physical Sciences and Earth Sciences University of Messina Messina98166 Italy Institute of Applied and Computational Mathematics Foundation for Research and Technology GR 700 13 Heraklion Crete Greece Instituto de Ciencia de Materiales de Madrid CSIC Cantoblanco Madrid Spain Department of Physics Oakland University RochesterMI48309 United States Department of Electrical and Information Engineering Politecnico di Bari Bari Italy

The study of thermodynamics of topological defects is an important challenge to understand their underlying physics. Among them, magnetic skyrmions have a leading role for their physical properties and potential applications in storage and neuromorphic computing. In this paper, the thermodynamic statistics of magnetic skyrmions is derived. It is shown that the skyrmion free energy can be modelled via a parabolic function and the diameters statistics obeys the Maxwell-Boltzmann distribution. This allows for making an analogy between the behavior of the distribution of skyrmion diameters statistics and the diluted gas Maxwell-Boltzmann molecules distribution at thermodynamical equilibrium. The calculation of the skyrmion configurational entropy, due to thermally-induced changes of size and shape of the skyrmion, is essential for the determination of thermal fluctuations of the skyrmion energy around its average value. These results can be employed to advance the field of skyrmionics. Copyright © 2019, The Authors. All rights reserved.

关键词： Magnetism

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Micromagnetic understanding of the skyrmion Hall angle current dependence in perpendicularly magnetized ferromagnets

引用

Physical Review B 2018年第22期98卷 224418-224418页

作者： Riccardo Tomasello Anna Giordano Stefano Chiappini Roberto Zivieri Giulio Siracusano Vito Puliafito Israa Medlej Aurelio La Corte Bruno Azzerboni Mario Carpentieri Zhongming Zeng Giovanni Finocchio Institute of Applied and Computational Mathematics FORTH GR-70013 Heraklion-Crete Greece Department of Mathematical and Computer Sciences Physical Sciences and Earth Sciences University of Messina I-98166 Messina Italy Istituto Nazionale di Geofisica e Vulcanologia Via di Vigna Murata 605 I-00143 Roma Italy Department of Electric Electronic and Computer Engineering University of Catania I-95125 Catania Italy Department of Engineering University of Messina I-98166 Messina Italy Department of Electrical and Information Engineering Politecnico di Bari I-70125 Bari Italy Key Laboratory of Nanodevices and Applications Suzhou Institute of Nano-tech and Nano-bionics Chinese Academy of Sciences Ruoshui Road 398 Suzhou 215123 People's Republic of China

The understanding of the dynamical properties of skyrmions is a fundamental aspect for the realization of a competitive skyrmion based technology beyond complementary metal-oxide semiconductors. Most of the theoretical approaches are based on the approximation of a rigid skyrmion. However, thermal fluctuations can drive a continuous change of the skyrmion size via the excitation of thermal modes. Here, by taking advantage of the Hilbert-Huang transform, we demonstrate that at least two thermal modes can be excited which are nonstationary in time. In addition, one limit of the rigid skyrmion approximation is that this hypothesis does not allow for correctly describing the recent experimental evidence of skyrmion Hall angle dependence on the amplitude of the driving force, which is proportional to the injected current. In this paper, we show that, in an ideal sample, the combined effect of fieldlike and dampinglike torques on a breathing skyrmion can indeed give rise to such a current dependent skyrmion Hall angle. While here we design and control the breathing mode of the skyrmion, our results can be linked to the experiments by considering that the thermal fluctuations and/or disorder can excite the breathing mode. We also develop a generalized Thiele equation and propose an experiment to validate our findings.

关键词： Skyrmions Spintronics Multilayer thin films Micromagnetic modeling

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Weighted graphlets and deep neural networks for protein structure classification

arXiv

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arXiv 2019年

作者： Guo, Hongyu Newaz, Khalique Emrich, Scott Milenković, Tijana Li, Jun Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States Department of Computer Science and Engineering University of Notre Dame Notre DameIN46556 United States Eck Institute for Global Health University of Notre Dame Notre DameIN46556 United States Interdisciplinary Center for Network Science & Applications University of Notre Dame Notre DameIN46556 United States Department of Electrical Engineering & Computer Science University of Tennessee KnoxvilleTN37996 United States

As proteins with similar structures often have similar functions, analysis of protein structures can help predict protein functions and is thus important. We consider the problem of protein structure classification, which computationally classifies the structures of proteins into pre-defined groups. We develop a weighted network that depicts the protein structures, and more importantly, we propose the first graphlet-based measure that applies to weighted networks. Further, we develop a deep neural network (DNN) composed of both convolutional and recurrent layers to use this measure for classification. Put together, our approach shows dramatic improvements in performance over existing graphlet-based approaches on 36 real datasets. Even comparing with the state-of-the-art approach, it almost halves the classification error. In addition to protein structure networks, our weighted-graphlet measure and DNN classifier can potentially be applied to classification of other weighted networks in computational biology as well as in other domains. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

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Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings

arXiv

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arXiv 2018年

作者： Oguz, Erdal C. Socolar, Joshua E.S. Steinhardt, Paul J. Torquato, Salvatore School of Mechanical Engineering Sackler Center for Computational Molecular and Materials Science Tel Aviv University Tel Aviv Israel Physics Department Duke University DurhamNC27708 United States Department of Physics Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Center for Cosmology and Particle Physics Department of Physics New York University New YorkNY10003 United States Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

We consider the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long wavelength fluctuations in a broad class of one-dimensional substitution tilings. We present a simple argument that predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and confirm with numerical computations that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra, and limit-periodic tilings. Tilings with quasiperiodic or singular continuous spectra can be constructed with α arbitrarily close to any given value between −1 and 3. Limit-periodic tilings can be constructed with α between −1 and 1 or with Fourier intensities that approach zero faster than any power law. Copyright © 2018, The Authors. All rights reserved.

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Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification

arXiv

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arXiv 2024年

作者： Menon, Karthik Zanoni, Andrea Khan, Owais Geraci, Gianluca Nieman, Koen Schiavazzi, Daniele E. Marsden, Alison L. Stanford School of Medicine StanfordCA United States Institute for Computational and Mathematical Engineering Stanford University StanfordCA United States Department of Electrical Computer and Biomedical Engineering Toronto Metropolitan University TorontoON Canada Center for Computing Research Sandia National Laboratories AlbuquerqueNM United States Division of Cardiovascular Medicine Stanford School of Medicine StanfordCA United States Department of Radiology Stanford School of Medicine StanfordCA United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States Department of Bioengineering Stanford University StanfordCA United States

Background: Non-invasive simulations of coronary hemodynamics have improved clinical risk stratification and treatment outcomes for coronary artery disease, compared to relying on anatomical imaging alone. However, simulations typically use empirical approaches to distribute total coronary flow amongst the arteries in the coronary tree, which ignores patient variability, the presence of disease, and other clinical factors. Further, uncertainty in the clinical data often remains unaccounted for in the modeling pipeline. Objective: We present an end-to-end uncertainty-aware pipeline to (1) personalize coronary flow simulations by incorporating vessel-specific coronary flows as well as cardiac function;and (2) predict clinical and biomechanical quantities of interest with improved precision, while accounting for uncertainty in the clinical data. Methods: We assimilate patient-specific measurements of myocardial blood flow from clinical CT myocardial perfusion imaging to estimate branch-specific coronary artery flows. Simulated noise in the clinical data is used to estimate the joint posterior distributions of the model parameters using adaptive Markov Chain Monte Carlo sampling. Additionally, the posterior predictive distribution for the relevant quantities of interest is determined using a new approach combining multi-fidelity Monte Carlo estimation with non-linear, data-driven dimensionality reduction. This leads to improved correlations between high- and low-fidelity model outputs. Results: Our framework accurately recapitulates clinically measured cardiac function as well as branch-specific coronary flows under measurement noise uncertainty. We observe substantial reductions in confidence intervals for estimated quantities of interest compared to single-fidelity Monte Carlo estimation and state-of-the-art multi-fidelity Monte Carlo methods. This holds especially true for quantities of interest that showed limited correlation between the low- and high-fidelity model

关键词： Monte Carlo methods

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Optimal undirectional amplification induced by optical gain in optomechanical systems

arXiv

引用

arXiv 2019年

作者： Song, L.N. Zheng, Qiang Xu, Xun-Wei Jiang, Cheng Li, Yong Beijing Computational Science Research Center Beijing100193 China School of Mathematics Guizhou Normal University Guiyang550001 China Department of Applied Physics East China Jiaotong University Nanchang330013 China School of Physics and Electronic Electrical Engineering Huaiyin Normal University Huai’an223300 China Synergetic Innovation Center for Quantum Effects and Applications Hunan Normal University Changsha410081 China

We propose a three-mode optomechanical system to realize optical nonreciprocal transmission with unidirectional amplification, where the system consists of two coupled cavities and one mechanical resonator which interacts with only one of the cavities. Additionally, the optical gain is introduced into the optomechanical cavity. It is found that for a strong optical input, the optical transmission coefficient can be greatly amplified in a particular direction and suppressed in the opposite direction. The expressions of the optimal transmission coefficient and the corresponding isolation ratio are given analytically. Our results pave a way to design high-quality nonreciprocal devices based on optomechanical *** Codes 81V80 Copyright © 2019, The Authors. All rights reserved.

关键词： Light transmission

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