检索结果-内蒙古大学图书馆

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

学校读者我要写书评

暂无评论

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

Automatic 3D Registration of Dental CBCT and Face Scan Data using 2D Projection Images

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Park, Hyoung Suk Hyun, Chang Min Lee, Sang-Hwy Seo, Jin Keun Jeon, Kiwan National Institute for Mathematical Sciences Daejeon34047 Korea Republic of School of Mathematics and Computing Computational Science and Engineering Yonsei University Seoul03722 Korea Republic of Department of Oral and Maxillofacial Surgery Oral Science Research Center College of Dentistry Yonsei University Seoul03722 Korea Republic of

This paper presents a fully automatic registration method of dental cone-beam computed tomography (CBCT) and face scan data. It can be used for a digital platform of 3D jaw-teeth-face models in a variety of applications, including 3D digital treatment planning and orthognathic surgery. Difficulties in accurately merging facial scans and CBCT images are due to the different image acquisition methods and limited area of correspondence between the two facial surfaces. In addition, it is difficult to use machine learning techniques because they use face-related 3D medical data with radiation exposure, which are difficult to obtain for training. The proposed method addresses these problems by reusing an existing machine-learning-based 2D landmark detection algorithm in an open-source library and developing a novel mathematical algorithm that identifies paired 3D landmarks from knowledge of the corresponding 2D landmarks. A main contribution of this study is that the proposed method does not require annotated training data of facial landmarks because it uses a pre-trained facial landmark detection algorithm that is known to be robust and generalized to various 2D face image models. Note that this reduces a 3D landmark detection problem to a 2D problem of identifying the corresponding landmarks on two 2D projection images generated from two different projection angles. Here, the 3D landmarks for registration were selected from the sub-surfaces with the least geometric change under the CBCT and face scan environments. For the final fine-tuning of the registration, the Iterative Closest Point method was applied, which utilizes geometrical information around the 3D landmarks. The experimental results show that the proposed method achieved an averaged surface distance error of 0.74 mm for three pairs of CBCT and face scan *** Codes 92C55, 15A04, 62F10 © 2023, CC BY.

关键词： Iterative methods

Self-propulsion dynamics of small droplets on general surfaces with curvature gradient

学校读者我要写书评

暂无评论

arXiv 2021年

作者： Chen, Yujuan Xu, Xianmin LSEC Institute of Computational Mathematics and Scientific/Engineering Computing NCMIS AMSS Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We study theoretically the self-propulsion dynamics of a small droplet on general curved surfaces by a variational approach. A new reduced model is derived based on careful computations for the capillary energy and the viscous dissipation in the system. The model describes quantitatively the spontaneous motion of a liquid droplet on general surfaces. In particular, it recovers previous models for droplet motion on the outside surface of a cone. In this case, we derive a scaling law of the displacement s ∼ t1/3 of a droplet with respect to time t by asymptotic analysis. Theoretical results are in good agreement with experiments in previous literature without adjusting the friction coefficient in the model. Copyright © 2021, The Authors. All rights reserved.

关键词： Asymptotic analysis

Adversarially robust clustering with optimality guarantees

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Jana, Soham Yang, Kun Kulkarni, Sanjeev The Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States The Data Science Institute Center For Research Computing Southern Methodist University DallasTX United States The Department of Operations Research and Financial Engineering Princeton University PrincetonNJ United States

We consider the problem of clustering data points coming from sub-Gaussian mixtures. Existing methods that provably achieve the optimal mislabeling error, such as the Lloyd algorithm, are usually vulnerable to outliers. In contrast, clustering methods seemingly robust to adversarial perturbations are not known to satisfy the optimal statistical guarantees. We propose a simple robust algorithm based on the coordinatewise median that obtains the optimal mislabeling rate even when we allow adversarial outliers to be present. Our algorithm achieves the optimal error rate in constant iterations when a weak initialization condition is satisfied. In the absence of outliers, in fixed dimensions, our theoretical guarantees are similar to that of the Lloyd algorithm. Extensive experiments on various simulated and public datasets are conducted to support the theoretical guarantees of our *** Codes 62G30, 62G35, 62H30 Copyright © 2023, The Authors. All rights reserved.

关键词： Clustering algorithms

Improved multifidelity Monte Carlo estimators based on normalizing flows and dimensionality reduction techniques

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Zanoni, Andrea Geraci, Gianluca Salvador, Matteo Menon, Karthik Marsden, Alison L. Schiavazzi, Daniele E. Institute for Computational and Mathematical Engineering Stanford University StanfordCA United States Center for Computing Research Sandia National Laboratories AlbuquerqueNM United States Pediatric Cardiology Stanford University StanfordCA United States Bioengineering Stanford University StanfordCA United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States

We study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches. Copyright © 2023, The Authors. All rights reserved.

关键词： Probability distributions

ASYMPTOTIC BEHAVIOR OF THE PRINCIPAL EIGENVALUE OF A LINEAR SECOND ORDER ELLIPTIC OPERATOR WITH LARGE ADVECTION AND GENERAL BOUNDARY CONDITIONS

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Peng, Rui Zhang, Guanghui Zhou, Maolin School of Mathematical Sciences Zhejiang Normal University Zhejiang Jinhua321004 China School of Mathematics and Statistics 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 Chern Institute of Mathematics and LPMC Nankai University Tianjin300071 China

Consider the eigenvalue problem of a linear second order elliptic operator: − D∆ − 2α∇m(x) · ∇ + V (x) = λ in Ω, complemented by the Dirichlet boundary condition or the following general Robin boundary condition: (Formula Presented) is a bounded smooth domain, n(x) is the unit exterior normal to ∂Ω at x ∈ ∂Ω, D > 0 and α > 0 are, respectively, the diffusion and advection coefficients, m ∈ C2(Ω), V ∈ C(Ω), β ∈ C(∂Ω) are given functions, and β allows to be positive, sign-changing or negative. In [41], the asymptotic behavior of the principal eigenvalue of the above eigenvalue problem as D → 0 or D → ∞ was studied. In this paper, when N ≥ 2, under proper conditions on the advection function m, we establish the asymptotic behavior of the principal eigenvalue as α → ∞, and when N = 1, we obtain a complete characterization for such asymptotic behavior provided m0 changes sign at most finitely many times. Our results complement or improve those in [4, 7, 44] and also partially answer some questions raised in [4]. © 2023, CC0.

关键词： Advection

Asymptotic Behavior of the Principal Eigenvalue of a Linear Second Order Elliptic Operator with Large Advection and General Boundary Conditions

学校读者我要写书评

暂无评论

SSRN

SSRN 2023年

In this paper, we consider asymptotic behavior of the principal eigenvalue of some second order elliptic operator with general boundary conditions. For $N=1$, we provide a complete characterization of the asymptotic behavior, assuming that $m'$ changes sign at most finitely many times. Our findings not only improve upon the previous work in \cite{BHN2005,CL2008,PZ2018}, but also partially address some of the open questions posed in \cite{BHN2005}. Furthermore, our results elucidate the novel influence of boundary conditions on such asymptotics. To achieve these results, we develop several sophisticated techniques to overcome the new difficulties posed by the problems under consideration. © 2023, The Authors. All rights reserved.

关键词： Advection

Uncertainty Quantification of Fiber Orientation and Epicardial Activation

学校读者我要写书评

暂无评论

Uncertainty Quantification of Fiber Orientation and Epicardi...

Computers in Cardiology (CinC)

作者： Lindsay C Rupp Anna Busatto Jake A Bergquist Karli Gillette Akil Narayan Gernot Plank Rob S MacLeod Scientific Computing and Imaging Institute University of Utah SLC UT USA Nora Eccles Cardiovascular Research and Training Institute University of Utah SLC UT USA Department of Biomedical Engineering University of Utah SLC UT USA Institute of Biophysics Medical University of Graz Graz Austria Department of Mathematics University of Utah SLC UT USA

Predictive models and simulations of cardiac function require accurate representations of anatomy, often to the scale of local myocardial fiber structure. However, acquiring this information in a patient-specific manner is challenging. Moreover, the impact of physiological variability in fiber orientation on simulations of cardiac activation is poorly understood. To explore these effects, we implemented bi-ventricular activation simulations using rule-based fiber algorithms and robust uncertainty quantification techniques to generate detailed maps of model variability. Specifically, we utilized polynomial chaos expansion, enabling efficient exploration with reduced computational demand through an emulator function approximating the underlying forward model. Our study focused on examining the epicardial activation sequences of the heart in response to six stimuli locations and five metrics of activation. Our findings revealed that physiological variability in fiber orientation does not significantly affect the location of activation features, but it does impact the overall spread of activation. We observed low variability near the earliest activation sites, but high variability across the rest of the epicardial surface. We conclude that the level of accuracy of myocardial fiber orientation required for simulation depends on the specific goals of the model and the related research or clinical goals.

关键词：

The macroscopic finite-difference scheme and modified equations of the general propagation multiple-relaxation-time lattice Boltzmann model

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Chen, Ying Liu, Xi Chai, Zhenhua Shi, Baochang School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Organization Hubei Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Organization Hubei Wuhan430074 China

In this paper, we first present the general propagation multiple-relaxation-time lattice Boltzmann (GPMRT-LB) model and obtain the corresponding macroscopic finite-difference (GPMFD) scheme on conservative moments. Then based on the Maxwell iteration method, we conduct the analysis on the truncation errors and modified equations (MEs) of the GPMRT-LB model and GPMFD scheme at both diffusive and acoustic scalings. For the nonlinear anisotropic convection-diffusion equation (NACDE) and Navier-Stokes equations (NSEs), we also derive the first- and second-order MEs of the GPMRT-LB model and GPMFD scheme. In particular, for the one-dimensional convection-diffusion equation (CDE) with the constant velocity and diffusion coefficient, we can develop a fourth-order GPMRT-LB (F-GPMRT-LB) model and the corresponding fourth-order GPMFD (F-GPMFD) scheme at the diffusive scaling. Finally, two benchmark problems, Gauss hill problem and Poiseuille flow in two-dimensional space, are used to test the GPMRT-LB model and GPMFD scheme, and it is found that the numerical results are not only in good agreement with corresponding analytical solutions, but also have a second-order convergence rate in space. Additionally, a numerical study on one-dimensional CDE also demonstrates that the F-GPMRT-LB model and F-GPMFD scheme can achieve a fourth-order accuracy in space, which is consistent with our theoretical analysis. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations