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Random-walk shielding-potential viscosity model for warm dense metals

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arXiv 2021年

作者： Cheng, Yuqing Liu, Haifeng Hou, Yong Meng, Xujun Li, Qiong Liu, Yu Gao, Xingyu Yuan, Jianmin Song, Haifeng Wang, Jianguo School of Mathematics and Physics University of Science and Technology Beijing Beijing100083 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100094 China Department of Physics College of Liberal Arts and Sciences National University of Defense Technology Changsha410073 China Graduate School China Academy of Engineering Physics Beijing100193 China

We develop a novel model, called the "random-walk shielding-potential viscosity model" (RWSP-VM) that introduces the statistics of random-walk ions and the Debye shielding effect to describe the viscosities of warm dense metals. The viscosities of several metals with low to high atomic number (Be, Al, Fe, and U) are calculated using the analytical expression of RWSP-VM. Additionally, we simulate the viscosities of Fe and Be by employing the Langevin molecular dynamics (MD) and classical MD, while the MD data for Al and U are obtained from a previous work. The results of the RWSP-VM are in good agreement with the MD results, which validates the proposed model. Furthermore, we compare the RWSP-VM with the one-component plasma model and Yukawa viscosity model and show that the three models yield results in excellent agreement with each other in the regime where the RWSP-VM is applicable. These results indicate that the RWSP-VM is a universal, accurate, and highly efficient model for calculating the viscosity of metals in the warm dense state. The code of the proposed RWSP-VM is provided, and it is envisaged that it will have broad application prospects in numerous fields. © 2021, CC BY-NC-ND.

关键词： Shielding

Discovery of partial differential equations from highly noisy and sparse data with physics-informed information criterion

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arXiv 2022年

作者： Xu, Hao Zeng, Junsheng Zhang, Dongxiao BIC-ESAT ERE SKLTCS College of Engineering Peking University Beijing100871 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Southern University of Science and Technology Guangdong Shenzhen518055 China Department of Mathematics and Theories Peng Cheng Laboratory Guangdong Shenzhen518000 China

Data-driven discovery of PDEs has made tremendous progress recently, and many canonical PDEs have been discovered successfully for proof-of-concept. However, determining the most proper PDE without prior references remains challenging in terms of practical applications. In this work, a physics-informed information criterion (PIC) is proposed to measure the parsimony and precision of the discovered PDE synthetically. The proposed PIC achieves state-of-the-art robustness to highly noisy and sparse data on seven canonical PDEs from different physical scenes, which confirms its ability to handle difficult situations. The PIC is also employed to discover unrevealed macroscale governing equations from microscopic simulation data in an actual physical scene. The results show that the discovered macroscale PDE is precise and parsimonious, and satisfies underlying symmetries, which facilitates understanding and simulation of the physical process. The proposition of PIC enables practical applications of PDE discovery in discovering unrevealed governing equations in broader physical scenes. © 2022, CC BY-NC-ND.

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Machine-learning-based non-Newtonian fluid model with molecular fidelity

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Physical Review E 2020年第4期102卷 043309-043309页

作者： Huan Lei Lei Wu Weinan E Department of Computational Mathematics Science & Engineering and Department of Statistics & Probability Michigan State University East Lansing Michigan 48824 USA Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We introduce a machine-learning-based framework for constructing continuum a non-Newtonian fluid dynamics model directly from a microscale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the microscale polymer configurations and their macroscale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the microscale model, and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a generalized form of the objective tensor derivative that retains the microscale interpretations. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. Numerical results demonstrate the accuracy of DeePN2 where models based on empirical closures show limitations.

关键词： Learning Neuronal networks Complex fluids Non-Newtonian fluids Rheology Viscoelasticity Multiscale modeling

Dynamics, scaling behavior, and control of nuclear wrinkling

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arXiv 2022年

作者： Jackson, Jonathan A. Romeo, Nicolas Mietke, Alexander Burns, Keaton J. Totz, Jan F. Martin, Adam C. Dunkel, Jörn Alsous, Jasmin Imran Department of Biology Massachusetts Institute of Technology United States Graduate Program in Biophysics Harvard University United States Department of Mathematics Massachusetts Institute of Technology United States Department of Physics Massachusetts Institute of Technology United States School of Mathematics University of Bristol United Kingdom Center for Computational Biology Flatiron Institute Simons Foundation United States

The cell nucleus is enveloped by a complex membrane, whose wrinkling has been implicated in disease and cellular aging. The biophysical dynamics and spectral evolution of nuclear wrinkling during multicellular development remain poorly understood due to a lack of direct quantitative measurements. Here, we combine live-imaging experiments, theory, and simulations to characterize the onset and dynamics of nuclear wrinkling during egg development in the fruit fly, Drosophila melanogaster, when nurse cell nuclei increase in size and display stereotypical wrinkling behavior. A spectral analysis of three-dimensional high-resolution data from several hundred nuclei reveals a robust asymptotic power-law scaling of angular fluctuations consistent with renormalization and scaling predictions from a nonlinear elastic shell model. We further demonstrate that nuclear wrinkling can be reversed through osmotic shock and suppressed by microtubule disruption, providing tunable physical and biological control parameters for probing mechanical properties of the nuclear envelope. Our findings advance the biophysical understanding of nuclear membrane fluctuations during early multicellular development. Copyright © 2022, The Authors. All rights reserved.

关键词： Spectrum analysis

Interplay between breathing-mode distortions and magnetic order in rare-earth nickelates from ab initio magnetic models

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Physical Review B 2021年第5期104卷 054403-054403页

作者： Danis I. Badrtdinov Alexander Hampel Cyrus E. Dreyer Theoretical Physics and Applied Mathematics Department Ural Federal University 620002 Yekaterinburg Russia Center for Computational Quantum Physics Flatiron Institute 162 Fifth Avenue New York New York 10010 USA Department of Physics and Astronomy Stony Brook University Stony Brook New York 11794-3800 USA

We use density-functional theory calculations to explore the magnetic properties of perovskite rare-earth nickelates RNiO3 by constructing microscopic magnetic models containing all relevant exchange interactions via Wannierization and Green's function techniques. These models elucidate the mechanism behind the formation of antiferromagnetic order with the experimentally observed propagation vector, and explain the reason previous DFT plus Hubbard U calculations favored ferromagnetic order. We perform calculations of magnetic moments and exchange-coupling parameters for different amplitudes of the R1+ breathing-mode distortion, which results in expanded and compressed NiO6 octahedra. Our analysis shows that the strong competition between nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic couplings determine the magnetic ordering. The inclusion of spin-orbit coupling demonstrates that the magnetic anisotropy is very small, while the magnetic moments of the short bond nickel atoms tend to zero similar to the collinear case. Finally, we show that nickelates with larger rare-earth ions display overall stronger exchange couplings, resulting in a more stable antiferromagnetic phase. Our results provide a clear picture of the trends of the magnetic order across the nickelate series and give insights into the coupling between magnetic order and structural distortions.

关键词： Magnetic anisotropy Magnetic interactions Magnetic order Density functional theory Wannier function methods

IMPROVED EFFICIENCY OF MULTILEVEL MONTE CARLO FOR STOCHASTIC PDE THROUGH STRONG PAIRWISE COUPLING

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arXiv 2021年

作者： Chada, Neil K. Hoel, Håkon Jasra, Ajay Zouraris, Georgios E. Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Mathematics for Uncertainty Quantification RWTH Aachen University Aachen Germany Department of Mathematics and Applied Mathematics Voutes Campus Crete HeraklionGR-700 13 Greece

Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations. For many problems, it is well-known that strong pairwise coupling of numerical solutions in the multilevel hierarchy is needed to obtain efficiency gains. In this work, we show that strong pairwise coupling indeed is also important when MLMC is applied to stochastic partial differential equations (SPDE) of reaction-diffusion type, as it can improve the rate of convergence and thus improve tractability. For the MLMC method with strong pairwise coupling that was developed and studied numerically on filtering problems in [Chernov et al., Numer. Math., 147 (2021), 71-125], we prove that the rate of computational efficiency is higher than for existing methods. We also provide numerical comparisons with alternative coupling ideas on linear and nonlinear SPDE to illustrate the importance of this *** Codes 65C05, 65N35, 60H35, 65C30 © 2021, CC BY.

关键词： Monte Carlo methods

Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws

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arXiv 2021年

作者： Ranocha, Hendrik Schlottke-Lakemper, Michael Chan, Jesse Rueda-Ramírez, Andrés M. Winters, Andrew R. Hindenlang, Florian Gassner, Gregor J. Applied Mathematics University of Münster Germany High-Performance Computing Center Stuttgart University of Stuttgart Germany Computational and Applied Mathematics Rice University United States Department of Mathematics and Computer Science University of Cologne Germany Computational Mathematics Division of Applied Mathematics Linköping University Sweden Max Planck Institute for Plasma Physics NMPP division Garching Germany Department of Mathematics and Computer Science Center for Data and Simulation Science University of Cologne Germany

Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entropy stability. While these techniques increase the robustness of DG methods significantly, they are also computationally more demanding than standard weak form nodal DG methods. We present several implementation techniques to improve the efficiency of flux differencing DG methods that use tensor product quadrilateral or hexahedral elements, in 2D or 3D respectively. Focus is mostly given to CPUs and DG methods for the compressible Euler equations, although these techniques are generally also useful for GPU computing and other physical systems including the compressible Navier-Stokes and magnetohydrodynamics equations. We present results using two open source codes, *** written in Julia and FLUXO written in Fortran, to demonstrate that our proposed implementation techniques are applicable to different code bases and programming languages. Copyright © 2021, The Authors. All rights reserved.

关键词： Entropy

Characterizing the hyperuniformity of ordered and disordered two-phase media

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Physical Review E 2021年第1期103卷 012123-012123页

作者： Jaeuk Kim Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform two-phase heterogeneous media, which include composites, porous media, foams, cellular solids, colloidal suspensions, and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances σV2(R) and the associated hyperuniformity order metrics B¯V. This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements, and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we purposely restrict ourselves to a certain class of two-dimensional periodic cellular networks as well as periodic and disordered or irregular packings of circular disks, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have minimal values of the hyperuniformity order metrics B¯V across all volume fractions. On the other hand, for all packings of circular disks examined, the triangular-lattice packings have the smallest values of B¯V for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing of circular disks have the minimal values of the order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems with desirable bulk physical properties by inverse d

关键词： Patterns in complex systems

Random conical tilt reconstruction without particle picking in cryo-electron microscopy

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arXiv 2021年

作者： Lan, Ti-Yen Boumal, Nicolas Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Mathematics EPFL LausanneCH-1015 Switzerland Department of Mathematics Princeton University PrincetonNJ08544 United States

We propose a method to reconstruct the 3-D molecular structure from micrographs collected at just one sample tilt angle in the random conical tilt scheme in cryo-electron microscopy. Our method uses autocorrelation analysis on the micrographs to estimate features of the molecule which are invariant under certain nuisance parameters such as the positions of molecular projections in the micrographs. This enables us to reconstruct the molecular structure directly from micrographs, completely circumventing the need for particle picking. We demonstrate reconstructions with simulated data and investigate the effect of the missing-cone region. These results show promise to reduce the size limit for single particle reconstruction in cryo-electron microscopy. © 2021, CC BY.

关键词： Electron microscopes