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Machine learning potential assisted exploration of complex defect potential energy surfaces

npj computational Materials 2024年第1期10卷 3017-3023页

作者： Chao Jiang Chris A.Marianetti Marat Khafizov David H.Hurley Computational Mechanics and Materials Department Idaho National LaboratoryIdaho FallsID 83415USA Department of Applied Physics and Applied Mathematics Columbia UniversityNew YorkNY 10027USA Department of Mechanical and Aerospace Engineering The Ohio State UniversityColumbusOH 43210USA Materials Science and Engineering Department Idaho National LaboratoryIdaho FallsID 83415USA

Atomic-scale defects generated in materials under both equilibrium and irradiation conditions can significantly impact their physical and mechanical *** the energetically most favorable ground-state configurations of these defects is an important step towards the fundamental understanding of their influence on the performance of materials ranging from photovoltaics to advanced nuclear ***,using fluorite-structured thorium dioxide(ThO_(2))as an exemplar,we demonstrate how density functional theory and machine learning interatomic potential can be synergistically combined into a powerful tool that enables exhaustive exploration of the large configuration spaces of small point defect *** study leads to several unexpected discoveries,including defect polymorphism and ground-state structures that defy our physical *** physical origins of these unexpected findings are elucidated using a local cluster expansion model developed in this work.

关键词： properties defect potential

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Energy-Based Discontinuous Galerkin Difference Methods for Second-Order Wave Equations

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Communications on applied mathematics and Computation 2022年第3期4卷 855-879页

作者： Lu Zhang Daniel Appelö Thomas Hagstrom Department of Applied Physics and Applied Mathematics Columbia UniversityNew YorkNY 10027USA Department of Computational Mathematics Science and Engineering and Department of MathematicsMichigan State UniversityEast LansingMI 48824USA Department of Mathematics Southern Methodist UniversityDallasTX 75275USA

We combine the newly constructed Galerkin difference basis with the energy-based discontinuous Galerkin method for wave equations in second-order *** approximation properties of the resulting method are excellent and the allowable time steps are large compared to traditional discontinuous Galerkin *** one drawback of the combined approach is the cost of inversion of the local mass *** demonstrate that for constant coefficient problems on Cartesian meshes this bottleneck can be removed by the use of a modified Galerkin difference *** variable coefficients or non-Cartesian meshes this technique is not possible and we instead use the preconditioned conjugate gradient method to iteratively invert the mass *** a careful choice of preconditioner we can demonstrate optimal complexity,albeit with a larger constant.

关键词： Discontinuous Galerkin Galerkin difference Simultaneous diagonalization

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Character Modelling with Sketches and ODE-Based Shape Creation

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Numerical mathematics(Theory,Methods and Applications) 2023年第3期16卷 720-751页

作者： Ouwen Li Haibin Fu Shaojun Bian Xiaosong Yang Xiaogang Jin Andres Iglesias Algirdas Noreika Lihua You Jian Jun Zhang National Centre for Computer Animation Bournemouth UniversityUnited Kingdom State Key Lab of CAD&CG Zhejiang UniversityChina Department of Applied Mathematics and Computational Sciences University of CantabriaSpain Department of Information Science Toho UniversityJapan Indeform Ltd Lithuania

Character models have enormous applications in *** creation of detailed character models is an important *** paper proposes a new and easy-to-use technique to quickly create detailed character models from *** proposed technique consists of two main components:primitive deformer and shape *** this technique,2D silhouette contours of a character model are drawn or extracted from an image or ***,proper geometric primitives are selected and aligned with the corresponding 2D silhouette *** that,a primitive deformer is used to create a base mesh and three shape generators are used to add 3D details to the base *** primitive deformer and three shape generators are developed from ODE-driven *** primitive deformer deforms the aligned geometric primitives to exactly match the 2D silhouette contours in one view plane and obtains a base mesh of a character model consisting of deformed *** shape generators are used to add 3D details to the base mesh by creating local 3D *** experimental results demonstrate that the new technique can quickly create detailed 3D character models from sketches with few manual *** new technique is physics-based and easy to learn and use.

关键词： Sketch-based character modelling shape generators ordinary differential equations finite difference solution

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Predicting Student Success in mathematics Using Machine Learning Techniques: A Comparative Study of Algorithms 1

Predicting Student Success in Mathematics Using Machine Lear...

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1st International Conference on Innovative and Intelligent Information Technologies, IC3IT 2024

作者： Samia, Zouaoui Houda, Zouaoui Nour El Hareth, Mestour University of Batna 2 Computer Science Department Batna Algeria Linfi Laboratory of Biskra University Algeria University of Biskra Laboratory of Applied Mathematics Mathematics Department Algeria University of Batna 2 Mathematics Department Batna Algeria

ISBN: (纸本)9798331541064

Achieving low results in mathematics is a real and urgent concern, as mathematics is the foundation of science and technology, and any weakness in it reflects negatively on the progress of society in various ways. This study evaluates how different mathematics study methods affect students educational success and achievement. We employed three different machine learning models to analyze data related to mathematics study techniques and student outcomes. These methods included: support vector machine (SVM), A K-nearest neighbors (KNN), and Linear Regression (LR). The results showed that KNN provided the best accuracy rate with 97.6% and an F1-score of 96.7%. These results highlight the significant contribution of forming study groups and trying to cooperate with each other, this factor is considered important and influential in the success of students in mathematics. © 2024 IEEE.

关键词： Contrastive Learning

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Lie algebra and conservation laws for the time-fractional heat equation

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Transactions of the Royal Society of South Africa 2023年第3期78卷 227-240页

作者： Halder, Amlan K. Duba, C.T. Leach, P.G.L. Department of Mathematics Pondicherry University Puducherry India School of Computer Science and Applied Mathematics University of the Witwatersrand Johannesburg South Africa Institute for Systems Science Durban University of Technology Durban South Africa School of Mathematics Statistics and Computer Science University of KwaZulu-Natal Durban South Africa

The Lie symmetry method is applied to derive the point symmetries for the N-dimensional fractional heat equation. We find that the numbers of symmetries and Lie brackets are reduced significantly as compared to the integer order for all dimensions. In fact for integer order linear heat equation the number of solution symmetries is equal to the product of the order and space dimension, whereas for the fractional case, it is half of the product on the order and space dimension. The Lie algebras for the integer and fractional order equations are mentioned using the subsequent computations of Lie brackets and by inspection. Interestingly, it is observed that for the one-dimensional fractional heat equation, the Lie algebra obtained by inspection of symmetries is similar to the result obtained by computation of Lie brackets, which is (Formula presented.). The Lie algebra using the symmetries of the two-dimensional heat equation is observed to be (Formula presented.), whereas using the Lie brackets the algebra is deduced to be (Formula presented.). Hence, it can be concluded that the Lie algebra obtained from the nonzero Lie brackets can be conflated to the algebra which is obtained by inspection. Further, the subsequent Lie algebras are mentioned for the three and four-dimensional integer and fractional equations and the conservation laws are explicitly stated. © 2023 Royal Society of South Africa.

关键词： conservation laws fractional partial differential equations lie symmetries solutions

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Ultrahigh-resolution atomic localization via superposition of standing waves

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Communications in Theoretical Physics 2025年第3期77卷 57-65页

作者： Muhammad Idrees Ahmed S Hendy Zareen A Khan Institute of Nonlinear Physics and Department of Physics Zhejiang Normal UniversityJinhua 321004China Zhejiang Institute of Photoelectronics and Zhejiang Institute for Advanced Light Source Zhejiang Normal UniversityJinhua 321004China Department of Computational Mathematics and Computer Science Institute of Natural Sciences and MathematicsUral Federal University19 Mira St.Yekaterinburg 620002Russia Department of Mechanics and Mathematics Western Caspian UniversityBaku 1001Azerbaijan Department of Mathematical Sciences College of SciencePrincess Nourah Bint Abdulrahman UniversityPO Box 84428Riyadh 11671Saudi Arabia

In this study we theoretically demonstrate ultrahigh-resolution two-dimensional atomic localization within a three-levelλ-type atomic medium via superposition of asymmetric and symmetric standing wave *** analysis provides an understanding of the precise spatial localization of atomic positions at the atomic level,utilizing advanced theoretical approaches and principles of quantum *** dynamical behavior of a three-level atomic system is thoroughly analyzed using the density matrix formalism within the realm of quantum mechanics.A theoretical approach is constructed to describe the interaction between the system and external fields,specifically a control field and a probe *** absorption spectrum of the probe field is thoroughly examined to clarify the spatial localization of the atom within the proposed configuration.A theoretical investigation found that symmetric and asymmetric superposition phenomena significantly influence the localized peaks within a two-dimensional spatial ***,the emergence of one and two sharp localized peaks was observed within a one-wavelength *** observed notable influences of the intensity of the control field,probe field detuning and decay rates on atomic ***,we have achieved an unprecedented level of ultrahigh resolution and precision in localizing an atom within an area smaller thanλ/35×λ/*** findings hold promise for potential applications in fields such as Bose-Einstein condensation,nanolithography,laser cooling,trapping of neutral atoms and the measurement of center-of-mass wave functions.

关键词： ultrahigh resolution atom localization symmetric and asymmetric superposition probe absorption standing wave fields

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Mathematical model of COVID-19 dynamics in the presence of multiple controls

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Quality and Quantity 2024年第1期59卷 261-290页

作者： Akanni, J.O. Fatmawati Ajao, S. Asamoah, J.K.K. Abimbade, S.F. Department of Mathematical and Computing Sciences Koladaisi University Oyo State Ibadan Nigeria Department of Mathematics Faculty of Science and Technology Universitas Airlangga Surabaya 60115 Indonesia Department of Mathematics and Computer Science Elizade University Ondo State Ilara-Mokin Nigeria Department of Mathematics Saveetha School of Engineering SIMATS Chennai India Department of Mathematics Kwame Nkrumah University of Science and Technology Kumasi Ghana Department of Pure and Applied Mathematics Ladoke Akintola University of Technology Oyo State Ogbomoso Nigeria

The coronavirus disease 19 (COVID-19), caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-COV-2), is an infectious disease constituting the most significant challenge to human and socio-economic development across the globe. Many studies have been conducted to gain more knowledge on the dynamic spread of SARS-COV-2 in the community of people. In this study, a new mathematical model made up of a system of non-linear ODEs is designed and meticulously analyzed to understand the dynamics of transmission of COVID-19. Specific necessary properties exhibited by the COVID-19 model are examined through the theory of non-negativity and boundedness of solutions. The threshold parameter measuring the invasion potential of COVID-19 in the population is worked out by employing the Next Generation Matrix approach. The model is shown to have two endemic equilibria whenever basic reproduction number R₀<1. The analysis of the endemic equilibrium stability is explored using a suitably constructed Lyapunov function. It is shown that the COVID-19 model is globally asymptotically stable whenever the associated basic reproduction number is beyond unity. The Latin Hypercube Sampling or Partial Rank Correlation Coefficient is utilized to examine how parameter changes affect the COVID-19 spread in the population. Furthermore, the study considers six optimal control interventions to flatten the curve of the coronavirus pandemic in society. Numerical experiments of the COVID-19 model are executed in MatLab to corroborate the qualitative analysis of the model. © The Author(s), under exclusive licence to Springer Nature B.V. 2024.

关键词： 49J15 cost-effectiveness analysis COVID-19 Dynamical system LHS/PRCC Mathematical modelling Optimal control analysis Sensitivity analysis

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Hydrogen-Bonding Interactions from Nucleobase-Decorated Supramolecular Polymer: Synthesis, Self-Assembly and Biomedical Applications

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ACS Biomaterials science and Engineering 2024年第1期10卷 234-254页

作者： Ilhami, Fasih Bintang Birhan, Yihenew Simegniew Cheng, Chih-Chia Department of Natural Science Faculty of Mathematics and Natural Science Universitas Negeri Surabaya Surabaya60231 Indonesia Department of Chemistry College of Natural and Computational Sciences Debre Markos University Debre Markos00000 Ethiopia Graduate Institute of Applied Science and Technology National Taiwan University of Science and Technology Taipei10607 Taiwan

The fabrication of supramolecular materials for biomedical applications such as drug delivery, bioimaging, wound-dressing, adhesion materials, photodynamic/photothermal therapy, infection control (as antibacterial), etc. has grown tremendously, due to their unique properties, especially the formation of hydrogen bonding. Nevertheless, void space in the integration process, lack of feasibility in the construction of supramolecular materials of natural origin in living biological systems, potential toxicity, the need for complex synthesis protocols, and costly production process limits the actual application of nanomaterials for advanced biomedical applications. On the other hand, hydrogen bonding from nucleobases is one of the strategies that shed light on the blurred deployment of nanomaterials in medical applications, given the increasing reports of supramolecular polymers that promote advanced technologies. Herein, we review the extensive body of literature about supramolecular functional biomaterials based on nucleobase hydrogen bonding pertinent to different biomedical applications. It focuses on the fundamental understanding about the synthesis, nucleobase-decorated supramolecular architecture, and novel properties with special emphasis on the recent developments in the assembly of nanostructures via hydrogen-bonding interactions of nucleobase. Moreover, the challenges, plausible solutions, and prospects of the so-called hydrogen bonding interaction from nucleobase for the fabrication of functional biomaterials are outlined. © 2023 American Chemical Society

关键词： Hydrogen bonds

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An Iterative Thresholding Method for the Minimum Compliance Problem

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Communications in computational Physics 2023年第4期33卷 1189-1216页

作者： Luyu Cen Wei Hu Dong Wang Xiaoping Wang Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina The Program in Applied and Computational Mathematics Princeton UniversityPrincetonNew JerseyUSA School of Science and Engineering The Chinese University of Hong KongShenzhenGuangdong 518172China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big DataGuangdong 518172China

In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance *** material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimization problem by the principle of minimum complementary *** prove that the energy is decreasing in each *** effective continuation schemes are proposed to avoid trapping into the local *** results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.

关键词： Minimum compliance convolution thresholding linear elasticity

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Some mathematical aspects of Anderson localization:boundary effect,multimodality,and bifurcation

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Communications in Theoretical Physics 2022年第11期74卷 45-64页

作者： Chen Jia Ziqi Liu Zhimin Zhang Applied and Computational Mathematics Division Beijing Computational Science Research CenterBeijing 100193China Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China Department of Mathematics Wayne State UniversityDetroitMichigan 48202United States of America

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered *** we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary conditions using a probabilistic approach,and further investigate some mathematical aspects of Anderson localization that are rarely discussed ***,we observe that under the Neumann boundary condition,the low energy quantum states are localized on the boundary of the domain with high *** provide a detailed explanation of this phenomenon using the concept of extended subregions and obtain an analytical expression of this probability in the one-dimensional ***,we find that the quantum states may be localized in multiple different subregions with high probability in the one-dimensional case and we derive an explicit expression of this probability for various boundary ***,we examine a bifurcation phenomenon of the localization subregion as the strength of disorder *** critical threshold of bifurcation is analytically computed based on a toy model and the dependence of the critical threshold on model parameters is analyzed.

关键词： landscape spectrum eigenvalue eigenmode eigenfunction elliptic operator Schr?dinger operator confinement

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