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Self-driven configurational dynamics in frustrated spring-mass systems

Physical Review E 2024年第2期109卷 024219-024219页

作者： Ori Saporta-Katz Avraham Moriel Computer Science and Applied Mathematics Department Weizmann Institute of Science Rehovot 7610001 Israel Chemical and Biological Physics Department Weizmann Institute of Science Rehovot 7610001 Israel

Various physical systems relax mechanical frustration through configurational rearrangements. We examine such rearrangements via Hamiltonian dynamics of simple internally stressed harmonic four-mass systems. We demonstrate theoretically and numerically how mechanical frustration controls the underlying potential energy landscape. Then, we examine the harmonic four-mass systems' Hamiltonian dynamics and relate the onset of chaotic motion to self-driven rearrangements. We show such configurational dynamics may occur without strong precursors, rendering such dynamics seemingly spontaneous.

关键词： Classical mechanics Chaotic systems Hamiltonian systems Molecular dynamics Phase space dynamics

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Local order metrics for many-particle systems across length scales

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Physical Review Research 2024年第3期6卷 033262页

作者： Charles Emmett Maher Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2(R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri,Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d=1,2,3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato et al., Phys. Rev. X 11, 021028 (2021)] to devise even more sensitive order metrics.

关键词： Classical statistical mechanics

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A Short Note on Solving Partial Differential Equations Using Convolutional Neural Networks 27th

A Short Note on Solving Partial Differential Equations Using...

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27th International Conference on Domain Decomposition Methods in science and Engineering, DD 2022

作者： Grimm, Viktor Heinlein, Alexander Klawonn, Axel Department of Mathematics and Computer Science University of Cologne Weyertal 86-90 Koln50931 Germany Delft University of Technology Delft Institute of Applied Mathematics Mekelweg 4 Delft2628 CD Netherlands Center for Data and Simulation Science University of Cologne Cologne Germany

ISBN: (纸本)9783031507687

Solving partial differential equations (PDEs) is a common task in numerical mathematics and scientific computing. Typical discretization schemes, for example, finite element (FE), finite volume (FV), or finite difference (FD) methods, have the disadvantage that the computations have to be repeated once the boundary conditions (BCs) or the geometry change slightly;typical examples requiring the solution of many similar problems are time-dependent and inverse problems or uncertainty quantification. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Boundary conditions

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Deformation of the Heisenberg–Weyl algebra and the Lie superalgebra : exact solution for the quantum harmonic oscillator with a position-dependent mass

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The European Physical Journal Plus 2025年第4期140卷 1-13页

作者： Jafarov, E. I. Nagiyev, S. M. Van der Jeugt, J. Institute of Physics Ministry of Science and Education Baku Azerbaijan Department of Applied Mathematics Computer Science and Statistics Ghent University Gent Belgium

We propose a new deformation of the quantum harmonic oscillator Heisenberg–Weyl algebra with a parameter $$a>-1$$ . This parameter is introduced through the replacement of the homogeneous mass $$m_0$$ in the definition of the momentum operator $$\hat{p}_x$$ as well as in the creation–annihilation operators $${\hat{a}}^\pm$$ with a mass varying with position x. The realization of such a deformation is shown through the exact solution of the corresponding Schrödinger equation for the non-relativistic quantum harmonic oscillator within the canonical approach. The obtained analytical expression of the energy spectrum consists of an infinite number of equidistant levels, whereas the wavefunctions of the stationary states of the problem under construction are expressed through the Hermite polynomials. Then, the Heisenberg–Weyl algebra deformation is generalized to the case of the Lie superalgebra $$\mathfrak {osp}\left( {1|2} \right)$$ . It is shown that the realization of such a generalized superalgebra can be performed for the parabose quantum harmonic oscillator problem, the mass of which possesses a behavior completely overlapping with the position-dependent mass of the canonically deformed harmonic oscillator problem. This problem is solved exactly for both even and odd stationary states. It is shown that the energy spectrum of the deformed parabose oscillator is still equidistant; however, both even- and odd-state wavefunctions are now expressed through the Laguerre polynomials. Some basic limit relations recovering the canonical harmonic oscillator with constant mass are also discussed briefly.

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Effects of calendering state on coupled electrochemical-mechanical performance of silicon based composite electrodes

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Green Energy and Intelligent Transportation 2024年第5期3卷 34-41页

作者： Dawei Li Hongfei Wan Jiahui Liu Hainan Jiang Yikai Wang Junqian Zhang Yuejiu Zheng School of Mechanical Engineering University of Shanghai for Science and TechnologyShanghai 200093China Department of Engineering Physics Tsinghua UniversityBeijing100084China Department of Chemical and Materials Engineering University of KentuckyLexingtonKY 40506USA Shanghai Institute of Applied Mathematics and Mechanics School of Mechanics and Engineering ScienceShanghai UniversityShanghai 200444China

The super volume changes and severe mechanical degradation have been a hindrance in the wide application of silicon based composite electrodes in commercial lithium-ion batteries(LIBs).Calendering,one procedure in producing LIBs'electrodes,is indispensable to ensure low porosity and energy ***,the repercussions of the calendering process on the physical characteristics related to the behavior of silicon(Si)based electrodes during the electrochemical reaction have not been well ***,on account of the deformation characteristic of cantilever electrodes,an in-situ technique is employed to analyze the repercussions of calendering status on the coupled electro-chemo-mechanical *** the electrochemical cycling,Young's modulus and diffusion-induced stress in composite electrodes are *** results show that the swelling strain,the stress and the modulus of the Si-based electrode and the calendering degree are positively ***,the stress induced by diffusion in the active layer tends to increase in the stage of lithiation and reverses during the delithiation *** with the SEM analysis,we conclude that the calendering process can induce larger stress,driving the formation of cracks in *** findings can help understand how the calendering process could affect the capacity dissipating and lifetime of Si based electrodes.

关键词： Calendering degree In situ measurement Coupled electro-mechan-chemical properties Si composite electrode Stress evolution

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Position: Is machine learning good or bad for the natural sciences? 41

Position: Is machine learning good or bad for the natural sc...

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41st International Conference on Machine Learning, ICML 2024

作者： Hogg, David W. Villar, Soledad Center for Cosmology and Particle Physics Department of Physics New York University United States Max-Planck-Institut für Astronomie Heidelberg Germany Flatiron Institute New York United States Department of Applied Mathematics and Statistics Johns Hopkins University United States Mathematical Institute for Data Science Johns Hopkins University United States

Machine learning (ML) methods are having a huge impact across all of the sciences. However, ML has a strong ontology-in which only the data exist-and a strong epistemology-in which a model is considered good if it performs well on held-out training data. These philosophies are in strong conflict with both standard practices and key philosophies in the natural sciences. Here we identify some locations for ML in the natural sciences at which the ontology and epistemology are valuable. For example, when an expressive machine learning model is used in a causal inference to represent the effects of confounders, such as foregrounds, backgrounds, or instrument calibration parameters, the model capacity and loose philosophy of ML can make the results more trustworthy. We also show that there are contexts in which the introduction of ML introduces strong, unwanted statistical biases. For one, when ML models are used to emulate physical (or first-principles) simulations, they amplify confirmation biases. For another, when expressive regressions are used to label datasets, those labels cannot be used in downstream joint or ensemble analyses without taking on uncontrolled biases. The question in the title is being asked of all of the natural sciences;that is, we are calling on the scientific communities to take a step back and consider the role and value of ML in their fields;the (partial) answers we give here come from the particular perspective of physics. Copyright 2024 by the author(s)

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Optical Applications of DNA Nanotechnology

ACS APPLIED OPTICAL MATERIALS

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ACS applied OPTICAL MATERIALS 2025年第3期3卷 481-482页

作者： Zhang, Fei Gang, Oleg Department of Chemistry Rutgers University Newark New Jersey 07102 United States Department of Chemical Engineering Columbia University New York New York 10027 United States Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 United States Center for Functional Nanomaterials Brookhaven National Laboratory Upton New York 11973 United States Department of Chemical Engineering and Department of Applied Physics and Applied Mathematics Columbia University New York New York 10027 United States Center for Nanomedicine Institute for Basic Science (IBS) Seoul 03722 Republic of Korea Department of Nano Biomedical Engineering (NanoBME) Advanced Science Institute Yonsei University Seoul 03722 Republic of Korea

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ASYMPTOTICALLY COMPATIBLE SCHEMES FOR NONLINEAR VARIATIONAL MODELS VIA GAMMA-CONVERGENCE AND APPLICATIONS TO NONLOCAL PROBLEMS

arXiv

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arXiv 2024年

作者： Du, Qiang Scott, James M. Tian, Xiaochuan Department of Applied Physics and Applied Mathematics Data Science Institute Columbia University New YorkNY10027 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Department of Mathematics University of California San DiegoCA92093 United States

We present a study on asymptotically compatible Galerkin discretizations for a class of parametrized nonlinear variational problems. The abstract analytical framework is based on variational convergence, or Gamma-convergence. We demonstrate the broad applicability of the theoretical framework by developing asymptotically compatible finite element discretizations of some representative nonlinear nonlocal variational problems on a bounded domain. These include nonlocal nonlinear problems with classically-defined, local boundary constraints through heterogeneous localization at the boundary, as well as nonlocal problems posed on parameter-dependent domains. Copyright © 2024, The Authors. All rights reserved.

关键词： Galerkin methods

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Cubature Kalman Fusion Filtering Under Amplify-and-Forward Relays With Randomly Varying Channel Parameters

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IEEE/CAA Journal of Automatica Sinica 2025年第2期12卷 356-368页

作者： Jiaxing Li Zidong Wang Jun Hu Hongli Dong Hongjian Liu the Department of Applied Mathematics Harbin University of Science and Technology IEEE the Department of Computer Science Brunel University London the School of Automation Harbin University of Science and Technology the Artificial Intelligence Energy Research Institute Northeast Petroleum University the Heilongjiang Provincial Key Laboratory of Networking and Intelligent Control Northeast Petroleum University the National Key Laboratory of Continental Shale Oil of China Northeast Petroleum University the Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment Ministry of Education Anhui Polytechnic University the School of Mathematics and Physics Anhui Polytechnic University

In this paper, the problem of cubature Kalman fusion filtering(CKFF) is addressed for multi-sensor systems under amplify-and-forward(AaF) relays. For the purpose of facilitating data transmission, AaF relays are utilized to regulate signal communication between sensors and filters. Here, the randomly varying channel parameters are represented by a set of stochastic variables whose occurring probabilities are permitted to exhibit bounded uncertainty. Employing the spherical-radial cubature principle, a local filter under AaF relays is initially constructed. This construction ensures and minimizes an upper bound of the filtering error covariance by designing an appropriate filter gain. Subsequently, the local filters are fused through the application of the covariance intersection fusion rule. Furthermore, the uniform boundedness of the filtering error covariance's upper bound is investigated through establishing certain sufficient conditions. The effectiveness of the proposed CKFF scheme is ultimately validated via a simulation experiment concentrating on a three-phase induction machine.

关键词： Amplify-and-forward (AaF) relays covariance intersection fusion cubature Kalman filtering multi-sensor systems uniform boundedness

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Trust in and Adoption of Generative AI in University Education: Opportunities, Challenges, and Implications

Trust in and Adoption of Generative AI in University Educati...

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IEEE Education Engineering (EDUCON)

作者： Yue Zhang Pascal Reusch Department of Mathematics and Physics Hainan Bielefeld University of Applied Sciences Lingshui China Department of Engineering and Mathematics Center for Applied Data Science (CfADS) Bielefeld University of Applied Sciences and Arts (HSBI) Gütersloh Germany

ISBN: (数字)9798331539498

ISBN: (纸本)9798331539504

Generative AI has emerged as a transformative tool in the realm of higher education, offering a wealth of opportunities for personalized learning, automated feedback, and enhanced collaboration. However, its successful adoption within university environments is significantly dependent on the trust it earns from its users, particularly students. This study investigates the levels of trust and the adoption of Generative AI among students enrolled in both German and international study programs at Hochschule Bielefeld (HSBI) and its transnational partner, Hainan Bielefeld University of applied sciences (BiUH). Utilizing a comprehensive questionnaire, the research explores students' perceptions of the trustworthiness of Generative AI, their usage patterns, and their concerns regarding the ethical and academic implications of its use. Preliminary findings suggest that while students widely recognize the potential of Generative AI to improve learning outcomes and efficiency, the degree of trust in its reliability and fairness varies significantly. Key factors influencing this trust include the transparency of AI systems, the perceived accuracy of outputs, and concerns about bias and misuse. Students in international and cross-cultural programs face additional challenges, such as language barriers and cultural differences, which affect how AI is perceived and utilized. Ethical concerns, particularly regarding plagiarism and academic integrity, are prevalent across all groups, underscoring the need for clear institutional guidelines and policies. The findings highlight the importance of fostering AI literacy and providing support structures to build trust and encourage responsible use. Recommendations include the implementation of transparent AI tools, tailored training programs, and the development of ethical guidelines to ensure that Generative AI enhances education while upholding academic standards. This research provides actionable insights for universities aiming to i

关键词： Training Ethics Generative AI Plagiarism Learning automata Reliability Artificial intelligence Engineering education Standards Guidelines

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