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arXiv 2022年

作者： Song, Xinliang Zhang, Yue Zhou, Xiafeng Zhang, Chuang Guo, Zhaoli State Key Laboratory of Coal Combustion School of Energy and Power Engineering Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Department of Nuclear Engineering and Technology School of Energy and Power Engineering Huazhong University of Science and Technology Wuhan430074 China Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen518055 China

In this work, a steady discrete unified gas kinetic scheme (SDUGKS) is proposed to solve the steady radiative transfer equation (RTE), which is an improvement of the original SDUGKS [X. F. Zhou et al., J. Comput. Phys. 423, 109767 (2020)]. The trapezoidal rule other than the rectangular rule used in the original SDUGKS is adopted in the proposed method in the reconstruction of energy flux across cell interface, just as the unsteady DUGKS. By this way, the characteristic line length of the modified SDUGKS establishes a relationship with the Courant-Friedrichs-Lewy (CFL) number in the DUGKS, which guarantees the accuracy of the modified SDUGKS. Furthermore, the characteristic line length is no longer limited by the extinction coefficient like in original SDUGKS. As a result, the modified SDUGKS is more accurate and robust than original SDUGKS, and more efficient than the DUGKS for steady radiation problems. Furthermore, the smooth linear interpolation and the van Leer limiter are used for problems with smooth and discontinuous optical thicknesses, respectively. Several numerical tests with optical thickness varying from optical thin to thick are conducted to validate the present scheme. Numerical results demonstrate that the modified SDUGKS can serve as an effective tool in the study of multiscale steady radiative heat transfer in participating media. Copyright © 2022, The Authors. All rights reserved.

关键词： Radiative transfer

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Wave properties using displaced phase amplitude 3

Wave properties using displaced phase amplitude

引用

3rd International Conference on Natural and Environmental Sciences 2019, ICONES 2019

作者： Fadhiliani, D. Ramli, M. Rizal, S. Munzir, S. Syafwan, M. Doctor of Mathematics and Applied Science Study Program Universitas Syiah Kuala Banda Aceh Indonesia Department of Mathematics Universitas Syiah Kuala Banda Aceh Indonesia Department of Marine Sciences Faculty of Marine and Fisheries Universitas Syiah Kuala Banda Aceh Indonesia Department of Mathematics Faculty of Mathematics and Natural Sciences Universitas Andalas Padang Indonesia

Displaced phase-amplitude variable in polar form. This variable is used to investigate changes in amplitude in complex fields with phases that depend only on the position in the propagation. Soliton on Finite Background (SFB) which is an exact solution of Nonlinear Schrodinger (NLS) equation has been widely used in investigating wave propagation dynamics so that it is the basic for the proposed displaced phase-amplitude. Using displaced phase-amplitude, the results obtained can be described in Argand Diagrams. Wave equation used as a model is the Benjamin Bona Mahony (BBM) equation where the envelope of this wave evolves following the NLS equation. This wave is unidirectional long wave on the surface and has low amplitude characteristics. Step by step to obtain a SFB solution that contains displaced phase-amplitude described and displayed in an argand diagram. In additional, the envelope graph is given. © 2019 Published under licence by IOP Publishing Ltd.

关键词： Nonlinear equations

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Image Recovery from Rotational And Translational Invariants

Image Recovery from Rotational And Translational Invariants

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Nicholas F. Marshall Ti-Yen Lan Tamir Bendory Amit Singer Department of Mathematics Princeton University Princeton NJ USA The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA School of Electrical Engineering Tel Aviv University Tel Aviv Israel

ISBN: (数字)9781509066315

ISBN: (纸本)9781509066322

We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotational and translational invariants and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM.

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Editorial

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Journal of Biological Dynamics 2019年第sup1期13卷 1-1页

作者： Cushing, Jim Elaydi, Saber Department of Mathematics and Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ United States

The 6th International Conference on Mathematical Modelling and Analysis of Populations in Biology (ICMA-VI) was held at the University of Arizona, Tucson, Arizona USA on 20-22 October 2017. Plenary addresses were given by Henri Berestycki (Centre d'analyse et de mathématique sociales, Paris, France), Regis Ferriere (Ecology and Evolutionary Biology department, University of Arizona, Tucson, Arizona, USA), Rosie Fisher (National Center for Atmospheric Research Climate & Global Dynamics, Boulder, Colorado, USA), and Mercedes Pascual (department of Ecology and Evolution, University of Chicago, Chicago, Illinois, USA). The conference received support from the department of mathematics, University of Arizona; the department of Ecology and Evolutionary Biology, University of Arizona; the interdisciplinary program in applied mathematics, University of Arizona; and the Simon A. Levin Mathematical, Computational and Modeling Sciences Center, Arizona State University. [Extracted from the article]

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Hybrid Auxiliary Field Quantum Monte Carlo for Molecular Systems

arXiv

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arXiv 2022年

作者： Chen, Yixiao Zhang, Linfeng Weinan, E. Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States AI for Science Institute Beijing100080 China DP Technology Beijing100080 China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing100084 China Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

We propose a quantum Monte Carlo approach to solve the many-body Schrödinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum Monte Carlo, in a way that significantly alleviates the sign problem. In application to molecular systems, we obtain highly accurate results for configurations dominated by either dynamic or static electronic correlation. Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods

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New (αβγ)-incommensurate magnetic phase discovered in the MnCr2O4 spinel at low temperatures

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Physical Review B 2023年第14期107卷 144401-144401页

作者： M. Pardo-Sainz A. Toshima G. André J. Basbus G. J. Cuello V. Laliena T. Honda T. Otomo K. Inoue Y. Hosokoshi Y. Kousaka J. Campo Aragón Nanoscience and Materials Institute (CSIC – University of Zaragoza) and Condensed Matter Physics Department C/Pedro Cerbuna 12 50009 Zaragoza Spain Graduate School of Science Osaka Metropolitan University Osaka 599-8531 Japan Research Institute for Interdisciplinary Science Okayama University Okayama Japan Laboratoire Léon Brillouin Saclay France Centro Atómico Bariloche S. C. de Bariloche Rio Negro Argentine Institut Laue-Langevin Grenoble France Applied Mathematics Department of the University of Zaragoza Zaragoza Spain Institute of Materials Structure Science Tsukuba Japan Graduate School of Science Chirality Research Center and International Institute for Sustainability with Knotted Chiral Meta Matter Hiroshima University Japan Department of Physics and Electronics Osaka Metropolitan University Osaka 599-8531 Japan

The nuclear and magnetic structure of the spinel MnCr2O4 is reinvestigated by magnetization, specific heat, and neutron diffraction experiments at different temperatures. Four samples of this spinel synthesized under different atmospheres are analyzed. Through these experiments, a new magnetic phase, with propagation vector k⃗I2=(0.6597(1)0.5999(1)0.1996(2)), not previously reported, is identified below 18 K when the sample is synthesized under a reductive atmosphere. A possible explanation for the different magnetic ground states observed is given based on the competition among the main exchange interactions present in the system. Using the magnetic superspace group formalism, the symmetry of the nuclear and magnetic structures is determined. The presence of transverse conical magnetic structures in the lower-temperature phases allows for multiferroicity in this compound, and the electric polarization direction is determined for each magnetic phase.

关键词： Composition Crystal symmetry Magnetic interactions Magnetic order Magnetic phase transitions Specific heat Chiral magnets Multiferroics Spinels Neutron diffraction Neutron scattering

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An eXtended HDG method for Darcy-Stokes-Brinkman interface problems

arXiv

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arXiv 2020年

作者： Han, Yihui Wang, Xiao-Ping Xie, Xiaoping South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal University Guangzhou510630 China Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong School of Mathematics Sichuan University Chengdu610064 China

This paper proposes an interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method for Darcy-Stokes-Brinkman interface problems in two and three dimensions. The method uses piecewise linear polynomials for the velocity approximation and piecewise constants for both the velocity gradient and pressure approximations in the interior of elements inside the subdomains separated by the interface, uses piecewise constants for the numerical traces of velocity on the inter-element boundaries inside the subdomains, and uses piecewise constants or linear polynomials for the numerical traces of velocity on the interface. Optimal error estimates are derived for the interface-unfitted X-HDG scheme. Numerical experiments are provided to verify the theoretical results and the robustness of the proposed method. Copyright © 2020, The Authors. All rights reserved.

关键词： Galerkin methods

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

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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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An interface/boundary-unfitted eXtended HDG method for linear elasticity problems

arXiv

引用

arXiv 2020年

作者： Han, Yihui Wang, Xiao-Ping Xie, Xiaoping South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal University Guangzhou510630 China Department of Mathematics The Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong School of Mathematics Sichuan University Chengdu610064 China

An interface/boundary-unfitted eXtended hybridizable discontinuous Galerkin (X-HDG) method of arbitrary order is proposed for linear elasticity interface problems on unfitted meshes with respect to the interface and domain boundary. The method uses piecewise polynomials of degrees k (≥ 1) and k − 1 respectively for the displacement and stress approximations in the interior of elements inside the subdomains separated by the interface, and piecewise polynomials of degree k for the numerical traces of the displacement on the inter-element boundaries inside the subdomains and on the interface/boundary of the domain. Optimal error estimates in L2-norm for the stress and displacement are derived. Finally, numerical experiments confirm the theoretical results and show that the method also applies to the case of crack-tip domain. Copyright © 2020, The Authors. All rights reserved.

关键词： Crack propagation

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Digital Audio Watermarking by Amplitude Embedding System 15th

Digital Audio Watermarking by Amplitude Embedding System

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15th International Conference on Intelligent Information Hiding and Multimedia Signal Processing, IIH-MSP 2019, held in conjunction with the 12th International Conference on Frontiers of Information Technology, Applications and Tools, FITAT 2019

作者： Lin, Meng-Ju Zhao, Ming Chen, Shuo-Tsung Chen, Ching-Ju Department of Applied Mathematics Tunghai University No. 1727 Sec.4 Taiwan Boulevard Taichung Taiwan40704 Taiwan School of Computer Science Yangtze University Jingzhou CityHubei Province China College of Future Bachelor Program in Interdisciplinary Studies National Yunlin University of Science and Technology TaiwanYunlin64002 Taiwan National Yunlin University of Science and Technology TaiwanYunlin64002 Taiwan

ISBN: (纸本)9789811397134

This paper proposed an amplitude embedding system for digital audio watermarking in the wavelet domain. In this paper, the relationship between the watermarked coefficients and the original coefficients is first presented and then amplitude-based embedding rules are combined into an amplitude-based embedding system that incorporates a system state. For the embedding in this system, the information includes synchronization codes and the watermarks are embedded into the DWT lowest frequency sub-band coefficients which can be described by a matrix form. Moreover, the SNR is rewritten as a performance index which is a quadratic form. Then, a nonlinear function connecting the performance index and the embedding system is derived. Accordingly, an optimization-based embedding system is proposed. Finally, the Karush–Kuhn–Tucker (KKT) Theorem is used to obtain the optimal solution, which is an important formula for watermarking. In addition, the hidden information can be extracted without knowledge of the original audio. In the experiments, the performance of the proposed system is tested and the results verify the high SNR and strong robustness against multimedia signal processing or malicious attacks. © 2020, Springer Nature Singapore Pte Ltd.

关键词： Embeddings

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