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Phase-field modeling of dendritic growth with gas bubbles in the solidification of binary alloys

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arXiv 2024年

作者： Zhan, Chengjie Chai, Zhenhua Sun, Dongke Shi, Baochang Geng, Shaoning Jiang, Ping School of Mathematics and Statistics 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 Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China School of Mechanical Engineering Southeast University Nanjing211189 China The State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and Engineering Huazhong University of Science and Technology Wuhan430074 China

In this work, a phase-field model is developed for the dendritic growth with gas bubbles in the solidification of binary alloys. In this model, a total free energy for the complex gas-liquid-dendrite system is proposed through considering the interactions of gas bubbles, liquid melt and solid dendrites, and it can reduce to the energy for gas-liquid flows in the region far from the solid phase, while degenerate to the energy for thermosolutal dendritic growth when the gas bubble disappears. The governing equations are usually obtained by minimizing the total free energy, but here some modifications are made to improve the capacity of the conservative phase-field equation for gas bubbles and convection-diffusion equation for solute transfer. Additionally, through the asymptotic analysis of the thin-interface limit, the present general phase-field model for alloy solidification can match the corresponding free boundary problem, and it is identical to the commonly used models under a specific choice of model parameters. Furthermore, to describe the fluid flow, the incompressible Navier-Stokes equations are adopted in the entire domain including gas, liquid, and solid regions, where the fluid-structure interaction is considered by a simple diffuse-interface method. To test the present phase-field model, the lattice Boltzmann method is used to study several problems of gas-liquid flows, dendritic growth as well as the solidification in presence of gas bubbles, and a good performance of the present model for such complex problems is observed. © 2024, CC BY-NC-ND.

关键词： Solidification

A diffuse-interface lattice Boltzmann method for the dendritic growth with thermosolutal convection

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arXiv 2022年

作者： Zhan, Chengjie Chai, Zhenhua Shi, Baochang Jiang, Ping Geng, Shaoning Sun, Dongke School of Mathematics and Statistics 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 Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China The State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and Engineering Huazhong University of Science and Technology Wuhan430074 China School of Mechanical Engineering Southeast University Nanjing211189 China

In this work, we proposed a diffuse interface model for the dendritic growth with thermosolutal convection. In this model, the sharp boundary between the fluid and solid dendrite is replaced by a thin but nonzero thickness diffuse interface, which is described by the order parameter governed by the phase-field equation for the dendritic growth. The governing equations for solute and heat transfer are modified such that the previous special treatments for source term can be avoided. To solve the model for the dendritic growth with thermosolutal convection, we also developed a diffuse-interface multi-relaxation-time lattice Boltzmann (LB) method. In this method, the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction, and the treatment on the complex fluid-solid interface can be avoided. In addition, four LB models are developed for the phase-field equation, concentration equation, temperature equation and the Navier-Stokes equations in a unified framework. Finally, to test the present diffuse-interface LB method, we performed some simulations of the dendritic growth, and found that the numerical results are in good agreements with some previous works. © 2022, CC BY-NC-ND.

关键词： Navier Stokes equations

HOMOGENIZATION OF THE DISTRIBUTION-DEPENDENT STOCHASTIC ABSTRACT FLUID MODELS

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arXiv 2023年

作者： Chen, Junlong Qiu, Zhaoyang Tang, Yanbin School of Sciences Great Bay University Great Bay Institute for Advanced Study Dongguan523000 China School of Mathematics University of Science and Technology of China Anhui Hefei230026 China School of Applied Mathematics Nanjing University of Finance and Economics Nanjing210046 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, we study the homogenization of the distribution-dependent stochastic abstract fluid models by combining the two−scale convergence and martingale representative approach. A general framework of the homogenization research is established for stochastic abstract fluid models which are the type of nonlinear partial differential equations including the (distribution-dependent) stochastic Navier-Stokes equations, stochastic magneto-hydrodynamic equations, stochastic Boussinesq equations, stochastic micropolar equations, stochastic Allen-Cahn equations. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

Experimental and Theoretical Evidence of Novel 2d Β-Nis Nanostructures Based High-Performance Battery-Type Solid-State Supercapacitor

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SSRN

SSRN 2023年

作者： Singh, Diwakar Samtham, Manopriya Bisht, Neeta Choudhary, Ekta Kumar, Vikesh Jangir, Ravindra Sonnathi, Neeleshwar Hosmani, Santosh S. Katre, Ankita Devan, Rupesh S. Department of Metallurgy Engineering and Materials Science Indian Institute of Technology Indore Simrol Khandwa Road Indore453552 India Department of Scientific Computing Modeling and Simulation Savitribai Phule Pune University Pune411007 India University School of Basic and Applied Sciences Guru Gobind Singh Indraprastha University Delhi110078 India Accelerator Physics and Synchrotrons Utilization Division Raja Ramanna Centre for Advanced Technology Indore452013 India

Recently, quirky features and eccentric structures of transition metal sulfides have grasped great attention to remove roadblocks and unwrap fresh avenues for electrodes in energy storage devices. Herein, we developed a 2D beta phase nickel sulfide nanosheets (2D β-NiS NSs) electrode with remarkable enhancement in charge storage properties. When served as active electrode for electrochemical tests, 2D NiS NSs exhibited ultra-high capacitance of 2693 F/g at 1 mV/s and specific capacity of 219 mAh/g at 1A/g. The symmetric battery type solid-state supercapacitor device comprising 2D β-NiS NSs electrodes exhibits specific capacity of 83.43 mAh/g at 2 A/g over broad potential range of 0.7V with good cycling performance, and energy and power density of 28.9 Wh/kg (@ 2A/g) and 21 kW/kg (@ 6A/g), respectively. Complementary first-principles density functional theory (DFT) calculations accomplished to explore the electrolyte ion interactions with nickel sulfide nanostructures defining 2D NiS NSs as a potential candidate for real-time applications. © 2023, The Authors. All rights reserved.

关键词： Sulfur compounds

Three-dimensional coherent x-ray diffractive imaging from a single view

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Three-dimensional coherent x-ray diffractive imaging from a ...

Conference on Lasers and Electro-Optics (CLEO)

作者： Richard L. Sandberg Kevin S. Raines Sara Salha Huaidong Jiang Jose A. Rodríguez Benjamin P. Fahimian Henry C. Kapteyn Margaret M. Murnane Jincheng Du Jianwei Miao Department of Physics and JILA University of Colorado at Boulder Boulder CO USA Now at Physical Chemistry and Applied Spectroscopy Los Alamos National Laboratory Los Alamos NM USA Department of Physics and Astronomy and California NanoSystems Institute University of California Los Angeles CA USA Department of Physics and Astronomy and California NanoSystems Institute University of of California Los Angeles California USA Molecular Biology Institute University of California Los Angeles California USA Department of Materials Science & Engineering Center for Advanced Scientific Computing and Modeling University of North Texas Denton Texas USA

We demonstrate that high numerical aperture coherent diffractive imaging enables three-dimensional imaging from a single exposure angle under certain conditions. We demonstrate this technique, called ankylography, wit... 详细信息

ISBN: (纸本)9781557528896

关键词： X-ray imaging X-ray diffraction Optical imaging X-ray lasers Free electron lasers Image reconstruction Testing Apertures Ultrafast optics Image resolution

Freezing dynamics of wetting droplet under a uniform electric field

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arXiv 2024年

作者： Huang, Jiangxu Li, Hanqing Che, Jiaqi Chai, Zhenhua Wang, Lei Shi, Baochang School of Mathematics and Statistics 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 Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Marine Design & Research Institute of China China The State Key Laboratory of Digital Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China School of Mathematics and Physics China University of Geosciences Wuhan430074 China

Electrofreezing is a powerful technique that employs the electric field to control and enhance the freezing process. In this work, a phase-field-based lattice Boltzmann (LB) method is developed to study the electrofreezing process of sessile droplet on a cooled substrate. The accuracy of the present LB method is first validated through performing some simulations of the three-phase Stefan problem, the droplet freezing on a cold wall, and the droplet deformation under a uniform electric field. Then it is used to investigate the effect of an electric field on the freezing of a wetting droplet on a cold substrate, and the numerical results show that the electric field has a significant influence on the freezing time of the droplet mainly through changing the morphology of the droplet. In particular, under the effect of the electric field, the freezing time is increased for the droplet with a prolate pattern, while the freezing time of the droplet with an oblate pattern is decreased. These numerical results bring some new insights on the electrofreezing and provide a valuable guidance for the precise regulation of droplet freezing. Copyright © 2024, The Authors. All rights reserved.

关键词： Wetting

Spectral gap of sparse bistochastic matrices with exchangeable rows

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arXiv 2018年

作者： Bordenave, Charles Qiu, Yanqi Zhang, Yiwei Institut de Mathématiques de Marseille CNRS Aix-Marseille University 39 Rue Frédéric Joliot Curie Marseille13013 France Institute of Mathematics and Hua Loo-Keng Key Laboratory of Mathematics AMSS Chinese Academy of Sciences Beijing100190 China CNRS Institut de Mathématiques de Toulouse University of Toulouse III School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

We consider a random bistochastic matrix of size n of the form MQ where M is a uniformly distributed permutation matrix and Q is a given bistochastic matrix. Under sparsity and regularity assumptions on Q, we prove that the second largest eigenvalue of MQ is essentially bounded by the normalized Hilbert-Schmidt norm of Q when n grows large. We apply this result to random walks on random regular digraphs.60B20, 60C05, 05C80, 05C38 Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Simulations of fractal star cluster formation: I. new insights for measuring mass segregation of star clusters with substructure

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arXiv 2017年

作者： Yu, Jincheng Puzia, Thomas H. Lin, Congping Zhang, Yiwei Institute of Astrophysics Pontificia Universidad Católica de Chile Av. Vicuna Mackenna 4860 Macul Santiago7820436 National Astronomical Observatories Chinese Academy of Sciences 20A Datun Road Beijing100012 Center for Mathematical Science Huazhong University of Science and Technology 1037 Luoyu Road Wuhan4370074 Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology 1037 Luoyu road Wuhan430074 School of Mathematics and Statistics Huazhong University of Science and Technology 1037 Luoyu Road Wuhan4370074

We compare the existent methods including the minimum spanning tree based method and the local stellar density based method, in measuring mass segregation of star clusters. We find that the minimum spanning tree method reflects more the compactness, which represents the global spatial distribution of massive stars, while the local stellar density method reflects more the crowdedness, which provides the local gravitational potential information. It is suggested to measure the local and the global mass segregation simultaneously. We also develop a hybrid method that takes both aspects into account. This hybrid method balances the local and the global mass segregation in the sense that the predominant one is either caused either by dynamical evolution or purely accidental, especially when such information is unknown a priori. In addition, we test our prescriptions with numerical models and show the impact of binaries in estimating the mass segregation value. As an application, we use these methods on the Orion Nebula Cluster (ONC) observations and the Taurus cluster. We find that the ONC is significantly mass segregated down to the 20th most massive stars. In contrast, the massive stars of the Taurus cluster are sparsely distributed in many different subclusters, showing a low degree of compactness. The massive stars of Taurus are also found to be distributed in the high-density region of the subclusters, showing significant mass segregation at subcluster scales. Meanwhile, we also apply these methods to discuss the possible mechanisms of the dynamical evolution of the simulated substructured star clusters. Copyright © 2017, The Authors. All rights reserved.

关键词： Numerical methods

Lethe-DEM: An open-source parallel discrete element solver with load balancing

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arXiv 2021年

作者： Golshan, Shahab Munch, Peter Gassmöller, Rene Kronbichler, Martin Blaisa, Bruno Department of Chemical Engineering École Polytechique de Montréal PO Box 6079 Stn Centre-Ville MontréalQCH3C 3A7 Canada Continuum Simulations Institute of Material Systems Modeling Helmholtz-Zentrum Hereon GmbH Germany Max-Planck-Str. 1 Geesthacht21502 Germany Institute for Computational Mechanics Technical University of Munich Boltzmannstr. 15 Garching85748 Germany Department of Geological Sciences University of Florida GainesvilleFL United States Division of Scientific Computing Department of Information Technology Uppsala University Box 337 Uppsala75105 Sweden

Approximately 75% of the raw material and 50% of the products in the chemical industry are granular materials. The Discrete Element Method (DEM) provides detailed insights of phenomena at particle scale and it is therefore often used for modeling granular materials. However, because DEM tracks the motion and contact of individual particles separately, its computational cost increases non-linearly O(np log(np)) - O(n2p) depending on the algorithm) with the number of particles (np). In this article, we introduce a new open-source parallel DEM software with load balancing: Lethe-DEM. Lethe-DEM, a module of Lethe, consists of solvers for two-dimensional and three-dimensional DEM simulations. Load-balancing allows Lethe-DEM to significantly increase the parallel efficiency by ≈ 25 − 70% depending on the granular simulation. We explain the fundamental modules of Lethe-DEM, its software architecture, and the governing equations. Furthermore, we verify Lethe-DEM with several tests including analytical solutions and comparison with other software. Comparisons with experiments in a flat-bottomed silo, wedge-shaped silo, and rotating drum validate Lethe-DEM. We investigate the strong and weak scaling of Lethe-DEM with 1 ≤ nc ≤ 192 and 32 ≤ nc ≤ 320 processes, respectively, with and without load-balancing. The strong-scaling analysis is performed on the wedge-shaped silo and rotating drum simulations, while for the weak-scaling analysis, we use a dam break simulation. The best scalability of Lethe-DEM is obtained in the range of 5000 ≤ np/nc ≤ 15 000. Finally, we demonstrate that large scale simulations can be carried out with Lethe-DEM using the simulation of a three-dimensional cylindrical silo with np = 4.3 × 106 on 320 cores. Copyright © 2021, The Authors. All rights reserved.

关键词： Finite difference method