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arXiv 2021年

作者： Guo, Yue Dietrich, Felix Bertalan, Tom Doncevic, Danimir T. Dahmen, Manuel Kevrekidis, Ioannis G. Li, Qianxiao Department of Mathematics National University of Singapore 117543 Singapore Institut für Informatik TU München Boltzmannstr. 3 Garching b. München85748 Germany Department of Chemical and Biomolecular Engineering Whiting School of Engineering Johns Hopkins University 3400 North Charles Street BaltimoreMD21218 United States Forschungszentrum Jülich GmbH Jülich52425 Germany RWTH Aachen University Aachen52062 Germany Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Whiting School of Engineering Johns Hopkins University 3400 North Charles Street BaltimoreMD21218 United States Department of Mathematics National University of Singapore Singapore117543 Singapore Institute of High Performance Computing A*STAR 138632 Singapore

MSC Codes 65L06, 68T07, 65L05We study the learning of numerical algorithms for scientific computing, which combines mathematically driven, handcrafted design of general algorithm structure with a data-driven adaptation to specific classes of tasks. This represents a departure from the classical approaches in numerical analysis, which typically do not feature such learning-based adaptations. As a case study, we develop a machine learning approach that automatically learns effective solvers for initial value problems in the form of ordinary differential equations (ODEs), based on the Runge-Kutta (RK) integrator architecture. We show that we can learn high-order integrators for targeted families of differential equations without the need for computing integrator coefficients by hand. Moreover, we demonstrate that in certain cases we can obtain superior performance to classical RK methods. This can be attributed to certain properties of the ODE families being identified and exploited by the approach. Overall, this work demonstrates an effective learning-based approach to the design of algorithms for the numerical solution of differential equations. This can be readily extended to other numerical tasks. © 2021, CC BY.

关键词： Ordinary differential equations

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Phase equilibrium of water with hexagonal and cubic ice using the SCAN functional

arXiv

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arXiv 2021年

作者： Piaggi, Pablo Miguel Panagiotopoulos, Athanassios Z. Debenedetti, Pablo G. Car, Roberto Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemical and Biological Engineering Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Machine learning models are rapidly becoming widely used to simulate complex physicochemical phenomena with ab initio accuracy. Here, we use one such model as well as direct density functional theory (DFT) calculations to investigate the phase equilibrium of water, hexagonal ice (Ih), and cubic ice (Ic), with an eye towards studying ice nucleation. The machine learning model is based on deep neural networks and has been trained on DFT data obtained using the SCAN exchange and correlation functional. We use this model to drive enhanced sampling simulations aimed at calculating a number of complex properties that are out of reach of DFT-driven simulations and then employ an appropriate reweighting procedure to compute the corresponding properties for the SCAN functional. This approach allows us to calculate the melting temperature of both ice polymorphs, the driving force for nucleation, the heat of fusion, the densities at the melting temperature, the relative stability of ice Ih and Ic, and other properties. We find a correct qualitative prediction of all properties of interest. In some cases, quantitative agreement with experiment is better than for state-of-the-art semiempirical potentials for water. Our results also show that SCAN correctly predicts that ice Ih is more stable than ice Ic. Copyright © 2021, The Authors. All rights reserved.

关键词： Ice

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Nuclear Neural Networks: Emulating Late Burning Stages in Core Collapse Supernova Progenitors

arXiv

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arXiv 2025年

作者： Grichener, Aldana Renzo, Mathieu Kerzendorf, Wolfgang E. Farmer, Rob de Mink, Selma E. Bellinger, Earl Patrick Chan, Chi-Kwan Chen, Nutan Farag, Ebraheem Justham, Stephen Steward Steward Observatory Department of Astronomy University of Arizona 933 North Cherry Avenue TucsonAZ85721 United States Max Planck Institute for Astrophysics Karl-Schwarzschild-Str. 1 Garching85748 Germany Department of Physics Technion Haifa3200003 Israel Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States Department of Physics and Astronomy Michigan State University East LansingMI48824 United States Ludwig-Maximilians-Universitat Munchen Geschwister-Scholl-Platz 1 Munchen80539 Germany Department of Astronomy Yale University New HavenCT06511 United States Steward Observatory Department of Astronomy University of Arizona 933 North Cherry Avenue TucsonAZ85721 United States Data Science Institute University of Arizona 1230 N. Cherry Avenue TucsonAZ85721 United States Program in Applied Mathematics University of Arizona 617 North Santa Rita TucsonAZ85721 United States Machine Learning Research Lab Volkswagen AG Munich38440 Germany

One of the main challenges in modeling massive stars to the onset of core collapse is the computational bottleneck of nucleosynthesis during advanced burning stages. The number of isotopes formed requires solving a large set of fully-coupled stiff ordinary differential equations (ODEs), making the simulations computationally intensive and prone to numerical instability. To overcome this barrier, we design a nuclear neural network (NNN) framework with multiple hidden layers to emulate nucleosynthesis calculations and conduct a proof-of-concept to evaluate its performance. The NNN takes the temperature, density and composition of a burning region as input and predicts the resulting isotopic abundances along with the energy generation and loss rates. We generate training sets for initial conditions corresponding to oxygen core depletion and beyond using large nuclear reaction networks, and compare the predictions of the NNNs to results from a commonly used small net. We find that the NNNs improve the accuracy of the electron fraction by 280 − 660 % and the nuclear energy generation by 250 − 750 %, consistently outperforming the small network across all timesteps. They also achieve significantly better predictions of neutrino losses on relatively short timescales, with improvements ranging from 100 − 106 %. While further work is needed to enhance their accuracy and applicability to different stellar conditions, integrating NNN trained models into stellar evolution codes is promising for facilitating large-scale generation of core-collapse supernova (CCSN) progenitors with higher physical fidelity. © 2025, CC BY.

关键词： Nucleosynthesis

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Multi-hump Collapsing Solutions in the Nonlinear Schrödinger Problem: Existence, Stability and Dynamics

arXiv

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arXiv 2025年

作者： Chapman, S. Jon Kavousanakis, Mihalis Charalampidis, Efstathios G. Kevrekidis, Ioannis G. Kevrekidis, Panayotis G. Mathematical Institute University of Oxford AWB ROQ Woodstock Road OxfordOX2 6GG United Kingdom School of Chemical Engineering National Technical University of Athens Athens15780 Greece Department of Mathematics and Statistics Computational Science Research Center San Diego State University San DiegoCA92182-7720 United States Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States Department of Mathematics and Statistics University of Massachusetts AmherstMA01003-4515 United States Department of Physics University of Massachusetts AmherstMA01003 United States

In the present work we examine multi-hump solutions of the nonlinear Schrödinger equation in the blowup regime of the one-dimensional model with power law nonlinearity, bearing a suitable exponent of σ > 2. We find that families of such solutions exist for arbitrary pulse numbers, with all of them bifurcating from the critical case of σ = 2. Remarkably, all of them involve "bifurcations from infinity", i.e., the pulses come inward from an infinite distance as the exponent σ increases past the critical point. The position of the pulses is quantified and the stability of the waveforms is also systematically examined in the so-called "co-exploding frame". Both the equilibrium distance between the pulse peaks and the point spectrum eigenvalues associated with the multi-hump configurations are obtained as a function of the blowup rate G theoretically, and these findings are supported by detailed numerical computations. Finally, some prototypical dynamical scenarios are explored, and an outlook towards such multi-hump solutions in higher dimensions is provided. Copyright © 2025, The Authors. All rights reserved.

关键词： Schrodinger equation

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Spectral discovery of jointly smooth features for multimodal data

arXiv

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arXiv 2020年

作者： Dietrich, Felix Yair, Or Mulayoff, Rotem Talmon, Ronen Kevrekidis, Ioannis G. Department of Informatics Technical University of Munich Viterbi Faculty of Electrical Engineering Technion Israel Institute of Technology Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University JHMI

In this paper, we propose a spectral method for deriving functions that are jointly smooth on multiple observed manifolds. This allows us to register measurements of the same phenomenon by heterogeneous sensors, and to reject sensor-specific noise. Our method is unsupervised and primarily consists of two steps. First, using kernels, we obtain a subspace spanning smooth functions on each separate manifold. Then, we apply a spectral method to the obtained subspaces and discover functions that are jointly smooth on all manifolds. We show analytically that our method is guaranteed to provide a set of orthogonal functions that are as jointly smooth as possible, ordered by increasing Dirichlet energy from the smoothest to the least smooth. In addition, we show that the extracted functions can be efficiently extended to unseen data using the Nyström method. We demonstrate the proposed method on both simulated and real measured data and compare the results to nonlinear variants of the seminal Canonical Correlation Analysis (CCA). Particularly, we show superior results for sleep stage identification. In addition, we show how the proposed method can be leveraged for finding minimal realizations of parameter spaces of nonlinear dynamical *** Codes 46Nxx, 47Nxx, 35K08, 58C05 Copyright © 2020, The Authors. All rights reserved.

关键词： Orthogonal functions

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Effect of rotation on the onset of convection in magnetic nanofluids with magnetic field dependent viscosity

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AIP Conference Proceedings 2024年第1期3081卷

作者： Monika Arora Mustafa Danesh Mahesh Kumar Sharma Kamalpreet Kaur Department of Mathematics School of Chemical Engineering and Physical Sciences Lovely Professional University Phagwara-144411 Punjab India Department of Mathematics Kabul Education University Kabul Afganistan Department of Mathematics School of Basic and Applied Sciences Maharaja Agrasen University Baddi H.P. India Lambton College at Queen’s College of Business Technology and Public Safety Mississauga-L4Z 3E9 Ontario Canada

This paper deals with the effect of rotation on the onset of convection in magnetic nanofluids (MNF) with magnetic field dependent (MFD) viscosity using linear stability theory. As suggested by J. Buongiorno [1], Brownian motion and thermophoresis are important slip mechanisms in nanofluid. Since this work is based on MNF therefore, magnetophoresis is included as the third slip mechanism in addition to those mentioned above. Numerical method is employed along with MATLAB’s EIG function to solve the resulting eigen value problem. Analysis is done graphically for ester-based MNF (EMNF) and water-based MNF (WMNF) through neutral stability curves (NSCs) and Critical stability curves (CSCs) for rigid-free boundary condition (Bcs) in gravity environment. The most significant parameter here is Taylor number (TA) which investigates the effect of rotation and the analysis shows that system gets stabilized with increase in the value of TA.

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Universal mechanical response of metallic glasses during strain-rate-dependent uniaxial compression

arXiv

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arXiv 2022年

作者： Jin, Weiwei Datye, Amit Schwarz, Udo D. Shattuck, Mark D. O'Hern, Corey S. Department of Mechanical Engineering and Materials Science Yale University New HavenCT06520 United States Department of Chemical and Environmental Engineering Yale University New HavenCT06520 United States Benjamin Levich Institute Physics Department The City College of New York New YorkNY10031 United States Department of Physics Yale University New HavenCT06520 United States Department of Applied Physics Yale University New HavenCT06520 United States Graduate Program in Computational Biology and Bioinformatics Yale University New HavenCT06520 United States

Experimental data on the compressive strength σmax versus strain rate Ε eng for metallic glasses undergoing uniaxial compression shows significantly different behavior for different alloys. For some metallic glasses, σmax decreases with increasing Ε eng, for others, σmax increases with increasing Ε eng, and for others σmax versus Ε eng is nonmonotonic. Using numerical simulations of metallic glasses undergoing uniaxial compression at nonzero strain rate and temperature, we show that they obey a universal relation for the compressive strength versus temperature, which determines their mechanical response. At low Ε eng, increasing strain rate leads to increases in temperature and decreases in σmax∗, whereas at high Ε eng, increasing strain rate leads to decreases in temperature and increases in σmax∗. This non-monotonic behavior of σmax∗ versus temperature causes the nonmonotonic behavior of σmax∗ versus Ε eng. Variations in the internal dissipation change the characteristic strain rate at which the nonmonotonic behavior occurs. These results are general for a wide range of metallic glasses with different atomic interactions, damping coefficients, and chemical compositions. © 2022, CC BY.

关键词： Strain rate

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Observation of the dual quantum spin Hall insulator by density-tuned correlations in a van der Waals monolayer

arXiv

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arXiv 2024年

作者： Tang, Jian Ding, Thomas Siyuan Chen, Hongyu Gao, Anyuan Qian, Tiema Huang, Zumeng Sun, Zhe Han, Xin Strasser, Alex Li, Jiangxu Geiwitz, Michael Shehabeldin, Mohamed Belosevich, Vsevolod Wang, Zihan Wang, Yiping Watanabe, Kenji Taniguchi, Takashi Bell, David C. Wang, Ziqiang Fu, Liang Zhang, Yang Qian, Xiaofeng Burch, Kenneth S. Shi, Youguo Ni, Ni Chang, Guoqing Xu, Su-Yang Ma, Qiong Department of Physics Boston College Chestnut HillMA United States Division of Physics and Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University Singapore Singapore Department of Chemistry and Chemical Biology Harvard University CambridgeMA United States Department of Physics and Astronomy and California NanoSystems Institute University of California Los Angeles Los AngelesCA United States Beijing National Laboratory for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences Beijing China Department of Materials Science and Engineering Texas A&M University College StationTX United States Department of Physics and Astronomy University of Tennessee KnoxvilleTN United States Min H. Kao Department of Electrical Engineering and Computer Science University of Tennessee KnoxvilleTN United States Research Center for Electronic and Optical Materials National Institute for Materials Science Tsukuba Japan Research Center for Materials Nanoarchitectonics National Institute for Materials Science Tsukuba Japan Harvard John A. Paulson School of Engineering and Applied Sciences The Center for Nanoscale system Harvard University CambridgeMA United States Department of Physics Massachusetts Institute of Technology CambridgeMA United States CIFAR Azrieli Global Scholars program CIFAR Toronto Canada

The convergence of topology and correlations represents a highly coveted realm in the pursuit of novel quantum states of matter [1, 2]. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order [3- 10], not possible in quantum Hall and Chern insulator systems. However, the QSH insulator with quantized edge conductance remains rare, let alone that with significant correlations. In this work, we report a novel dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator that aligns with single-particle band structure calculations, manifesting enhanced nonlocal transport and quantized helical edge conductance. Interestingly, upon introducing electrons from charge neutrality, TaIrTe4 only shows metallic behavior in a small range of charge densities but quickly goes into a new insulating state, entirely unexpected based on TaIrTe4's single-particle band structure. This insulating state could arise from a strong electronic instability near the van Hove singularities (VHS), likely leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state, marked by the revival of nonlocal transport and quantized helical edge conduction. Our observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands via CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism [3-5, 11, 12]. Copyright © 2024, The Authors. All rights reserved.

关键词： Charge density waves

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High-efficiency and ultrastable solvent-free curable perovskite quantum dot inks for microLED and LED backlighting applications

引用

Nano Energy 2025年 142卷

作者： Loan Thi Ngo Yu-Ting Huang Cheng-Chieh Chang Hemant Verma Yen-Huei Lin Ching-Tai Kuo Ying-Chih Liao Chao-Cheng Kaun Ren-Jei Chung Ru-Shi Liu Department of Chemistry National Taiwan University Taipei 106 Taiwan Nano Science and Technology Program Taiwan International Graduate Program Academia Sinica and National Taiwan University Academia Road 128 Nankang Taipei 115 Taiwan Department of Chemical Engineering and Biotechnology National Taipei University of Technology Taipei 106 Taiwan Department of Physics National Taiwan University Taipei 106 Taiwan Research Center for Applied Sciences Academia Sinica Academia Road 128 Section 2 Nangang Taipei 11529 Taiwan Department of Chemical Engineering National Taiwan University Taipei 106 Taiwan

Metal lead halide perovskite quantum dots (PeQDs) exhibit exceptional optoelectronic properties, showing promise as components for solar cells, lighting, display, and anticounterfeiting devices. However, the instability of PeQDs, along with synthesis and storage methods that rely on hazardous solvents, has limited their potential for commercial applications. To overcome these obstacles, we introduce a solvent-free method for fabricating high-quality green and red CsPbX 3 PeQD (X = Br, I) ink. Using a fluidic system, we first obtained super-high photoluminescence quantum yield PeQDs (92 % for red CsPb(Br,I) 3 , and nearly 100 % for green CsPbBr 3 PeQDs). The uniform nonsolvent PeQD ink is fabricated by modifying the as-formed PeQD surface with a mixture of trimethoxysilane and 3-(trimethoxysilyl)propyl methacrylate silane coupling agents to form PeQDs@silane, then dispersing the PeQDs@silane in a UV-curable 1,6-hexanediol diacrylate monomer. Our solvent-free PeQD ink exhibits bright and stable green and red emissions with long-term stability, retaining 100 % PL intensity after 115 days for CsPbBr 3 and 78 days for CsPb(Br,I) 3 . The environment-friendly ink enables highly uniform and bright films for LED backlighting and patterns for micro-LED applications. With color coordinates near the red and green reference values, the PeQD films demonstrate a remarkable 100.28 % color gamut coverage in comparison with Rec. 2020. This scalable and environmentally friendly method provides a safer alternative than conventional solvent-based PeQD ink.

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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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