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Numerical homogenization of elastoplastic deformations of composite material with small proportion of inclusions

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Journal of Physics: Conference Series 2019年第1期1392卷

作者： Petr V. Sivtsev Aleksandr E. Kolesov Petr E. Zakharov Ying Yang Research Laboratory 'Multiscale Matheatical Modeling and Computing' Ammosov North-Eastern Federal University 58 Belinskogo 677000 Yakutsk Russia Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 Hunan China

Numerical simulation of the stress-strain state of a composite material may be difficult due to large computational complexity associated with a grid resolution of a large number of inclusions. To overcome the problem one may use the homogenization method. But for material with plastic properties, proper modeling of yield stress and hardening may be overcomplicated. In this work we use some simplification associated with a small proportion of inclusions and restriction of stress values by matrix material strength. As model problem, we use deformation of concrete deep beam reinforced with steel or basalt fiber inclusions. For the numerical solution, the finite element method was applied using the FEniCS computing platform.

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Phase-field modeling of two-dimensional solute precipitation/dissolution: Solid fingers and diffusion-limited precipitation

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arXiv 2018年

作者： Xu, Zhijie Meakin, Paul Computational Mathematics Group Fundamental and Computational Sciences Directorate Pacific Northwest National Laboratory RichlandWA99352 United States Center for Advanced Modeling and Simulation Idaho National Laboratory Idaho FallsID83415 United States Physics of Geological Processes University of Oslo Oslo0316 Norway Multiphase Flow Assurance Innovation Center Institute for Energy Technology Kjeller2027 Norway

Two-dimensional dendritic growth due to solute precipitation was simulated using a phase-field model reported earlier [Z. Xu and P. Meakin, J. Chem. Phys. 129, 014705 (2008)]. It was shown that diffusion-limited precipitation due to the chemical reaction at the solid-liquid interface posses similarities with diffusion-limited aggregation (DLA). The diffusion-limited precipitation is attained by setting the chemical reaction rate much larger compared to the solute diffusion to eliminate the effect of the interface growth kinetics. The phase-field simulation results were in reasonable agreement with the analytical solutions. The fractal solid fingers can be formed in the diffusion-limited precipitation and have a fractal dimension measured fd=1.68, close to 1.64, the fractal dimensionality of large square lattice diffusion-limited aggregation (DLA) clusters. Copyright © 2018, The Authors. All rights reserved.

关键词： Precipitation (chemical)

A dissipative particle dynamics model of biofilm growth

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arXiv 2018年

作者： Xu, Zhijie Meakin, Paul Tartakovsky, Alexandre Scheibe, Timothy D. Computational Mathematics Group Fundamental and Computational Sciences Directorate Pacific Northwest National Laboratory RichlandWA99352 United States Center for Advanced Modeling and Simulation Idaho National Laboratory Idaho FallsID83415 United States Physics of Geological Processes University of Oslo Oslo0316 Norway Multiphase Flow Assurance Innovation Center Institute for Energy Technology Kjeller2027 Norway Hydrology Technical Group Energy and Environment Directorate Pacific Northwest National Laboratory RichlandWA99352 United States

A dissipative particle dynamics (DPD) model for the quantitative simulation of biofilm growth controlled by substrate (nutrient) consumption, advective and diffusive substrate transport, and hydrodynamic interactions with fluid flow (including fragmentation and reattachment) is described. The model was used to simulate biomass growth, decay, and spreading. It predicts how the biofilm morphology depends on flow conditions, biofilm growth kinetics, the rheomechanical properties of the biofilm and adhesion to solid surfaces. The morphology of the model biofilm depends strongly on its rigidity and the magnitude of the body force that drives the fluid over the biofilm. Copyright © 2018, The Authors. All rights reserved.

关键词： Morphology

A Mathematical Study to Gout Symptoms

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Journal of Applied Mathematics and Physics 2018年第12期6卷 2579-2588页

作者： Shuixian Yan Victor Moreno Sanling Yuan Baojun Song Business School University of Shanghai for Science and Technology Shanghai China Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques Gannan Normal University Ganzhou China Simon A. Levin Mathematical Computational and Modeling Sciences Center Arizona State University Tempe AZ USA College of Science University of Shanghai for Science and Technology Shanghai China Department of Mathematical Sciences Montclair State University Montclair NJ USA

Gout is a form of inflammatory arthritis characterized by sharp pain and severe swelling that often causes severe physical disability. Gout is caused by the chronic elevation of uric acid levels in the blood and is known as the disease of kings due to its strong association with a diet rich in fructose and beer. Recent studies suggest that a high uric acid concentration is the result of a dynamical process that highlights the interactions between leptin production, insulin resistance, low muscle mass and a diet rich in fructose. Once individuals develop hyperuricemia, reach a high uric acid concentration in excess of 7 mg/dL for men and 6 mg/dL for women, they become susceptible to developing gout. We propose a novel dynamic system to analyze and determine the connections between a diet involving different levels of fructose (in both adult men and women in the U.S.) and the concentration of uric acid in the blood. Our model simulations suggest that adult males under a diet containing levels of fructose stimulating a 0.5 uric acid growth rate, could develop hyperuricemia after around 10,000 days, while it only takes women about 5000 days with a diet stimulating a 0.4 growth rate.

关键词： Gout Uric Acid Leptin Insulin Mathematical Models

Generalized nonequilibrium quantum transport of spin and pseudospins: Entanglements and topological phases

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arXiv 2018年

作者： Buot, Felix A. Rivero, Karla B. Otadoy, Roland E. S. Center for Simulation and Modeling College of Science George Mason University FairfaxVA22030 United States Department of Physics Laboratory of Computational Functional Materials Nanoscience and Nanotechnology University of San Carlos-Talamban Campus Talamban Cebu6000 Philippines C and Lb Research Institute Carmen Cebu6005 Philippines Physics Department College of Science and Mathematics And Western Mindanao State University Zamboanga City7000 Philippines

General nonequilibrium quantum transport equations are derived for a coupled system of charge carriers, Dirac spin, isospin (or valley spin), and pseudospin, such as either one of the band, layer, impurity, and boundary pseudospins. Limiting cases are obtained for one, two or three different kinds of spin ocurring in a system. We show that a characteristic integer number Ns determines the formal form of spin quantum transport equations, irrespective of the type of spins or pseudospins, as well as the maximal entanglement entropy. The results may shed a new perspective on the mechanism leading to zero modes and chiral/helical edge states in topological insulators, integer quantum Hall effect topological insulator (QHE-TI), quantum spin Hall effect topological insulator (QSHE-TI) and Kondo topological insulator (Kondo-TI). It also shed new light in the observed competing weak localization and antilocalization in spin-dependent quantum transport measurements. In particular, a novel mechanism of localization and delocalization, as well as the new mechanism leading to the onset of superconductivity in bilayer systems seems to emerge naturally from torque entanglements in nonequilibrium quantum transport equations of spin and pseudospins. Moreover, the general results may serve as a foundation for engineering approximations of the quantum transport simulations of spintronic devices based on graphene and other 2-D materials such as the transition metal dichalcogenides (TMDs), silicene, as well as based on topological materials exhibiting quantum spin Hall effects. The extension of the formalism to spincaloritronics and pseudo-spincaloritronics is straightforward. Copyright © 2018, The Authors. All rights reserved.

关键词： Quantum Hall effect

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

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arXiv 2020年

作者： Berre, Inga Boon, Wietse M. Flemisch, Bernd Fumagalli, Alessio Gläser, Dennis Keilegavlen, Eirik Scotti, Anna Stefansson, Ivar Tatomir, Alexandru Brenner, Konstantin Burbulla, Samuel Devloo, Philippe Duran, Omar Favino, Marco Hennicker, Julian Lee, I-Hsien Lipnikov, Konstantin Masson, Roland Mosthaf, Klaus Chiara Nestola, Maria Giuseppina Ni, Chuen-Fa Nikitin, Kirill Schädle, Philipp Svyatskiy, Daniil Yanbarisov, Ruslan Zulianp, Patrick Department of Mathematics University of Bergen Allégaten 41 Bergen5007 Norway Department of Mathematics KTH Royal Institute of Technology Lindstedtsvägen 25 Stockholm11428 Sweden Department of Hydromechanics and Modelling of Hydrosystems University of Stuttgart Pfaffenwaldring 61 Stuttgart70569 Germany Laboratory for Modeling and Scientific Computing MOX Politecnico di Milano p.za Leonardo da Vinci 32 Milano20133 Italy Department of Applied Geology Geosciences Center University of Göttingen Goldschmidtstrasse 3 Göttingen37077 Germany Department of Earth Sciences Uppsala University Villavägen 16 UppsalaS-75236 Sweden University of Côte d’Azur CNRS INRIA LJAD Nice France Institute of Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 Stuttgart70569 Germany FEC Universidade Estadual de Campinas Cidade Universitária R. Josiah Willard Gibbs 85 Campinas-SPCEP 13083-839 Brazil Institute of Earth Sciences University of Lausanne Building Geopolis UNIL-Mouline Lausanne1015 Switzerland Section de Mathématiques Université de Genève 2-4 rue du Lièvre CP 64 Genève1211 Switzerland Graduate Institute of Applied Geology National Central University Taiwan Center for Environmental Studies National Central University Taiwan Los Alamos National Laboratory New Mexico United States Department of Environmental Engineering Technical University of Denmark Bygningstorvet Building 115 Kgs. Lyngby2800 Denmark Numerical Simulation in Science Medicine and Engineering Group Institute of Computational Science Università della Svizzera italiana. Via G. Buffi 13 Lugano Ticino6900 Switzerland Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences Moscow Russia ETH Zürich Geothermal Energy and Geofluids Group Institute of Geophysics Zürich8092 Switzerland

Flow in fractured porous media occurs in the earth’s subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, we present a portfolio of four benchmark cases for single-phase flow in three-dimensional fractured porous media. The cases are specifically designed to test the methods’ capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases. Copyright © 2020, The Authors. All rights reserved.

关键词： Numerical methods

Weak doping dependence of the antiferromagnetic coupling between nearest-neighbor Mn2+ spins in (Ba1−xKx)(Zn1−yMny)2As2

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Physical Review B 2018年第10期97卷 104418-104418页

作者： M. A. Surmach B. J. Chen Z. Deng C. Q. Jin J. K. Glasbrenner I. I. Mazin A. Ivanov D. S. Inosov Institut für Festkörper- und Materialphysik TU Dresden D-01069 Dresden Germany Institute of Physics Chinese Academy of Sciences 100190 Beijing China Center for High Pressure Science and Technology Advanced Research Beijing 100094 China School of Physics University of Chinese Academy of Sciences Beijing 100049 China Collaborative Innovation Center of Quantum Matter Beijing 100049 China Department of Computational and Data Sciences/Center for Simulation and Modeling George Mason University 4400 University Drive Fairfax Virginia 22030 USA Code 6393 Naval Research Laboratory Washington DC 20375 USA Institut Laue-Langevin 71 avenue des Martyrs CS 20156 F-38042 Grenoble Cedex 9 France

Dilute magnetic semiconductors (DMS) are nonmagnetic semiconductors doped with magnetic transition metals. The recently discovered DMS material (Ba1−xKx)(Zn1−yMny)2As2 offers a unique and versatile control of the Curie temperature TC by decoupling the spin (Mn2+, S=5/2) and charge (K+) doping in different crystallographic layers. In an attempt to describe from first-principles calculations the role of hole doping in stabilizing ferromagnetic order, it was recently suggested that the antiferromagnetic exchange coupling J between the nearest-neighbor Mn ions would experience a nearly twofold suppression upon doping 20% of holes by potassium substitution. At the same time, further-neighbor interactions become increasingly ferromagnetic upon doping, leading to a rapid increase of TC. Using inelastic neutron scattering, we have observed a localized magnetic excitation at about 13 meV associated with the destruction of the nearest-neighbor Mn-Mn singlet ground state. Hole doping results in a notable broadening of this peak, evidencing significant particle-hole damping, but with only a minor change in the peak position. We argue that this unexpected result can be explained by a combined effect of superexchange and double-exchange interactions.

关键词： Ferromagnetism Magnetic semiconductors Inelastic neutron scattering

i-PI 2.0: A universal force engine for advanced molecular simulations

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arXiv 2018年

作者： Kapil, Venkat Rossi, Mariana Marsalek, Ondrej Petraglia, Riccardo Litman, Yair Spura, Thomas Cheng, Bingqing Cuzzocrea, Alice Meißner, Robert H. Wilkins, David M. Juda, Przemyslaw Bienvenue, Sébastien P. Fang, Wei Kessler, Jan Poltavsky, Igor Vandenbrande, Steven Wieme, Jelle Corminboeuf, Clemence Kühne, Thomas D. Manolopoulos, David E. Markland, Thomas E. Richardson, Jeremy O. Tkatchenko, Alexandre Tribello, Gareth A. van Speybroeck, Veronique Ceriotti, Michele Laboratory of Computational Science and Modeling Institute of Materials École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland Fritz Haber Institute of the Max Planck Society Theory Department Faradayweg 4-6 Berlin14195 Germany Physics and Materials Science Research Unit University of Luxembourg L-1511 Luxembourg Department of Chemistry Stanford University StanfordCA94305 United States Atomistic Simulation Centre School of Mathematics and Physics Queen’s University Belfast BelfastBT7 1NN United Kingdom Department of Chemistry and Center for Sustainable Systems Design University of Paderborn Warburger Str. 100 PaderbornD-33098 Germany Laboratory of Physical Chemistry ETH Zurich Zurich8093 Switzerland Center for Molecular Modeling Ghent University Zwijnaarde9052 Belgium Physical and Theoretical Chemistry Laboratory South Parks Road OxfordOX1 3QZ United Kingdom Laboratory for Computational Molecular Design Institute of Chemical Sciences and Engineering École Polytechnique Fédérale de Lausanne Lausanne1015 Switzerland Charles University Faculty of Mathematics and Physics Ke Karlovu 3 Prague 2121 16 Czech Republic

Progress in the atomic-scale modelling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by either solving the electronic structure problem explicitly, or by computing accurate approximations of the solution and by the development of techniques that use the Born-Oppenheimer (BO) forces to move the atoms on the BO potential energy surface. As a consequence of these developments it is now possible to identify stable or metastable states, to sample configurations consistent with the appropriate thermodynamic ensemble, and to estimate the kinetics of reactions and phase transitions. All too often, however, progress is slowed down by the bottleneck associated with implementing new optimization algorithms and/or sampling techniques into the many existing electronic-structure and empirical-potential codes. To address this problem, we are thus releasing a new version of the i-PI software. This piece of software is an easily extensible framework for implementing advanced atomistic simulation techniques using interatomic potentials and forces calculated by an external driver code. While the original version of the code[1] was developed with a focus on path integral molecular dynamics techniques, this second release of i-PI not only includes several new advanced path integral methods, but also offers other classes of algorithms. In other words, i-PI is moving towards becoming a universal force engine that is both modular and tightly coupled to the driver codes that evaluate the potential energy surface and its derivatives. Copyright © 2018, The Authors. All rights reserved.

关键词： Molecular dynamics

The Gibbs free energy of homogeneous nucleation: From atomistic nuclei to the planar limit

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arXiv 2017年

作者： Cheng, Bingqing Tribello, Gareth A. Ceriotti, Michele Laboratory of Computational Science and Modeling Institute of Materials Ecole Polytechnique Federale de Lausanne Lausanne1015 Switzerland Atomistic Simulation Centre School of Mathematics and Physics Queen's University Belfast BelfastBT7 1NN United Kingdom

In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such simulations can be determined unambiguously by using a Gibbs dividing surface and how the free energy as a function of the number of solid atoms in the nucleus can thus be extracted. We then show that the parameters of a model based on classical nucleation theory can be fit using the information contained in these free-energy profiles but that the parameters in such models are highly correlated. This correlation is unfortunate as it ensures that small errors in the computed free energy surface can give rise to large errors in the extrapolated properties of the fitted model. To resolve this problem we thus propose a method for fitting macroscopic nucleation models that uses simulations of planar interfaces and simulations of three-dimensional nuclei in tandem. We show that when the parameters of the macroscopic model are fitted in this way the numerical errors for the final fitted model are smaller and that the extrapolated predictions for large nuclei are thus more reliable. Copyright © 2017, The Authors. All rights reserved.

关键词： Nucleation