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Your search keyword '"Zhao, Xianliang"' showing total 239 results
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239 results on '"Zhao, Xianliang"'

1. Quantitative particle approximations of stochastic 2D Navier-Stokes equation

Author

Shao, Yufei and Zhao, Xianliang

Subjects
Mathematics - Probability, Mathematics - Analysis of PDEs
Abstract

In this article, we investigate an interacting particle system featuring random intensities, individual noise, and environmental noise, commonly referred to as stochastic point vortex model. The model serves as an approximation for the stochastic 2-dimensional Navier-Stokes equation. We establish a quantitative mean-field convergence for the stochastic 2-dimensional Navier-Stokes equation in the form of relative entropy. To address challenges posed by environmental noise, random intensities, and singular kernel, we compare relative entropy for conditional distributions, employing technology of disintegration and the relative entropy method developed by Jabin and Wang in [JW18]., Comment: 51 pages

Published
2024

4. Mean-field limit of Non-exchangeable interacting diffusions with singular kernels

Author

Wang, Zhenfu, Zhao, Xianliang, and Zhu, Rongchan

Subjects
Mathematics - Probability, Mathematics - Analysis of PDEs
Abstract

The mean-field limit of interacting diffusions without exchangeability, caused by weighted interactions and non-i.i.d. initial values, are investigated. The weights could be signed and unbounded. The result applies to a large class of singular kernels including the Biot-Savart law. We demonstrate a flexible type of mean-field convergence, in contrast to the typical convergence of $\frac{1}{N}\sum_{i=1}^N\delta_{X_i}$. More specifically, the sequence of signed empirical measure processes with arbitrary uniform $l^r$-weights, $r>1$, weakly converges to a coupled PDE's, such as the dynamics describing the passive scalar advected by the 2D Navier-Stokes equation. Our method is based on a tightness/compactness argument and makes use of the systems' uniform Fisher information. The main difficulty is to determine how to propagate the regularity properties of the limits of empirical measures in the absence of the DeFinetti-Hewitt-Savage theorem for the non-exchangeable case. To this end, a sequence of random measures, which merges weakly with a sequence of weighted empirical measures and has uniform Sobolev regularity, is constructed through the disintegration of the joint laws of particles., Comment: 34 pages

Published
2022

7. Gaussian fluctuations for interacting particle systems with singular kernels

Author

Wang, Zhenfu, Zhao, Xianliang, and Zhu, Rongchan

Subjects
Mathematics - Probability, Mathematics - Analysis of PDEs, 60 Probability theory and stochastic processes
Abstract

We consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized Ornstein-Uhlenbeck process. Our result considerably extends classical results to singular kernels, including the Biot-Savart law. The result applies to the point vortex model approximating the 2D incompressible Navier-Stokes equation and the 2D Euler equation. We also obtain Gaussianity and optimal regularity of the limiting Ornstein-Uhlenbeck process. The method relies on the martingale approach and the Donsker-Varadhan variational formula, which transfers the uniform estimate to some exponential integrals. Estimation of those exponential integrals follows by cancellations and combinatorics techniques and is of the type of large deviation principle., Comment: 46 pages. Submit version with more references and acknowledgments

Published
2021

18. Study on Changes of Visual Function Before and After 24 hours Simulated Flight Visual Fatigue Protection

Author

Tian, Dawei, Mo, Fengfeng, Yan, Xiaobin, Zhang, Yange, Wu, Feng, Chen, Shan, Zhao, Xianliang, Huang, Jing, Deng, Lue, Angrisani, Leopoldo, Series Editor, Arteaga, Marco, Series Editor, Panigrahi, Bijaya Ketan, Series Editor, Chakraborty, Samarjit, Series Editor, Chen, Jiming, Series Editor, Chen, Shanben, Series Editor, Chen, Tan Kay, Series Editor, Dillmann, Rüdiger, Series Editor, Duan, Haibin, Series Editor, Ferrari, Gianluigi, Series Editor, Ferre, Manuel, Series Editor, Hirche, Sandra, Series Editor, Jabbari, Faryar, Series Editor, Jia, Limin, Series Editor, Kacprzyk, Janusz, Series Editor, Khamis, Alaa, Series Editor, Kroeger, Torsten, Series Editor, Li, Yong, Series Editor, Liang, Qilian, Series Editor, Martín, Ferran, Series Editor, Ming, Tan Cher, Series Editor, Minker, Wolfgang, Series Editor, Misra, Pradeep, Series Editor, Möller, Sebastian, Series Editor, Mukhopadhyay, Subhas, Series Editor, Ning, Cun-Zheng, Series Editor, Nishida, Toyoaki, Series Editor, Pascucci, Federica, Series Editor, Qin, Yong, Series Editor, Seng, Gan Woon, Series Editor, Speidel, Joachim, Series Editor, Veiga, Germano, Series Editor, Wu, Haitao, Series Editor, Zamboni, Walter, Series Editor, Zhang, Junjie James, Series Editor, Long, Shengzhao, editor, and Dhillon, Balbir S., editor

Published
2022
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43. The role of ferroptosis in fish inflammation

Author

Gao, Feng, primary, Shi, Xiaowei, additional, Pei, Chao, additional, Zhao, Xianliang, additional, Zhu, Lei, additional, Zhang, Jie, additional, Li, Li, additional, Li, Chen, additional, and Kong, Xianghui, additional

Published
2022
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